Aloe dichotoma (Quiver tree) occurs in the arid regions of Namaqualand and Bushman land in South Africa, and in arid regions of southern Namibia. The Quiver trees are not only threatened by agricultural expansion, ove...Aloe dichotoma (Quiver tree) occurs in the arid regions of Namaqualand and Bushman land in South Africa, and in arid regions of southern Namibia. The Quiver trees are not only threatened by agricultural expansion, overgrazing, and mining;but also by climate changes and droughts. Previous studies show that Quiver trees are very sensitive to environmental changes, and do not respond well to extreme hot and dry conditions. This study investigates the current status of the Quiver tree within its existing environment, and also assesses the projected future changes of the Quiver tree habitat under different climatic scenarios. It provided evidence regarding the importance of the study to understanding the climate change impacts on the Quiver tree and its geographical response to climate changes.展开更多
Using the connection between McKay quiver and Loewy matrix, and the properties of characteristic polynomial of Loewy matrix, we give a generalized way to determine the McKay quiver for a finite subgroup of a generaliz...Using the connection between McKay quiver and Loewy matrix, and the properties of characteristic polynomial of Loewy matrix, we give a generalized way to determine the McKay quiver for a finite subgroup of a generalized linear group.展开更多
Let A be a basic,connected finite dimensional algebra over an algebraically closed field with finite representation type, α(A) be the maximum of set consisting of numbers of indecomposable summands in the middle term...Let A be a basic,connected finite dimensional algebra over an algebraically closed field with finite representation type, α(A) be the maximum of set consisting of numbers of indecomposable summands in the middle term of Auslander Reiten sequences in mod A. In this paper we show that if α(A)=1, then Γ A contains oriented cycles if and only if Γ A contains DT r periodic modules. When α(A)2 we give counterexamples to the assertion.展开更多
We study four-dimensional quiver gauge models from F-theory compactified on fourfolds with hyper-K¨ahler structure.Using intersecting complex toric surfaces,we derive a class of N =1 quivers with charged fundamen...We study four-dimensional quiver gauge models from F-theory compactified on fourfolds with hyper-K¨ahler structure.Using intersecting complex toric surfaces,we derive a class of N =1 quivers with charged fundamental matter placed on external nodes.The emphasis is on how local Calabi–Yau equations solve the corresponding physical constraints including the anomaly cancelation condition.Concretely,a linear chain of SU(N) groups with flavor symmetries has been constructed using polyvalent toric geometry.展开更多
The representations of the Dynkin quivers and the corresponding Euclidean quivers are treated in many books. These notes provide three building blocks for dealing with representations of Dynkin （and Euclidean） quive...The representations of the Dynkin quivers and the corresponding Euclidean quivers are treated in many books. These notes provide three building blocks for dealing with representations of Dynkin （and Euclidean） quivers. They should be helpful as part of a direct approach to study representations of quivers, and they shed some new light on properties of Dynkin and Euclidean quivers.展开更多
As generalizations of quivers of type A,Igusa et al.introduced continuous quivers of type A.In this paper,we generalize BGP reflection functors to continuous quivers of type A,and we give another realization of the re...As generalizations of quivers of type A,Igusa et al.introduced continuous quivers of type A.In this paper,we generalize BGP reflection functors to continuous quivers of type A,and we give another realization of the reflection functor.展开更多
We single out a class of translation quivers and prove combinatorially that the translation quivers in this class are coils. These coils form a class of special coils. They are easier to visualize, but still show all ...We single out a class of translation quivers and prove combinatorially that the translation quivers in this class are coils. These coils form a class of special coils. They are easier to visualize, but still show all the strange behaviour of general coils, and contain quasi-stable tubes as special examples.展开更多
In this paper, we prove that there exists no sectional cycle in a translation quiver under certain conditions. So, we generalize Dautista and Smalφ's corresponding result on AR-quiver of an artin algebra.
We single out a class of translation quivers and prove that the translation quivers in this class are generalized multicoils. These generalized multicoils form a class of special generalized multicoils. They are easie...We single out a class of translation quivers and prove that the translation quivers in this class are generalized multicoils. These generalized multicoils form a class of special generalized multicoils. They are easier to visualize, but still show all the strange behaviours of generalized multicoils, and contain quasi-stable tubes as special examples.展开更多
We give sufficient conditions and necessary conditions on duality preservability of Auslander-Reiten quivers of derived categories and cluster categories over hereditary algebras. of generalized path algebras as cleft...We give sufficient conditions and necessary conditions on duality preservability of Auslander-Reiten quivers of derived categories and cluster categories over hereditary algebras. of generalized path algebras as cleft Meantime, we characterize the condition extensions of path algebras.展开更多
We consider stable representations of non-Dynkin quivers with respect to a central charge.These attract a lot of interest in mathematics and physics since they can be identified with so-called BPS states.Another motiv...We consider stable representations of non-Dynkin quivers with respect to a central charge.These attract a lot of interest in mathematics and physics since they can be identified with so-called BPS states.Another motivation is the work of Dimitrov et al.on the phases of stable representations of the generalized Kronecker quiver.One aim is to explain for general Euclidean and wild quivers the behavior of phases of stable representations well known in some examples.In addition,we study especially the behavior of preinjective,postprojective and regular indecomposable modules.We show that the existence of a stable representation with self-extensions implies the existence of infinitely many stables without self-extensions for rigid central charges.In this case the phases of the stable representations approach one or two limit points.In particular,the phases are not dense in two arcs.The category of representations of acyclic quivers is a special case of rigid Abelian categories which show this behavior for rigid central charges.展开更多
In this paper,we introduce the m-Cartan matrix and observe that some properties of the quadratic form associated to the Cartan matrix of an Euclidean diagram can be generalized to the m-Cartan matrix of a McKay quiver...In this paper,we introduce the m-Cartan matrix and observe that some properties of the quadratic form associated to the Cartan matrix of an Euclidean diagram can be generalized to the m-Cartan matrix of a McKay quiver.We also describe the McKay quiver for a finite abelian subgroup of a special linear group.展开更多
Using the quiver technique we construct a class of non-graded bi-Frobenius algebras.We also classify a class of graded bi-Frobenius algebras via certain equations of structure coefficients.
For a classical group G over a field F together with a finite-order automorphism θ that acts compatibly on F, we describe the fixed point subgroup of θ on G and the eigenspaces of θ on the Lie algebra g in terms of...For a classical group G over a field F together with a finite-order automorphism θ that acts compatibly on F, we describe the fixed point subgroup of θ on G and the eigenspaces of θ on the Lie algebra g in terms of cyclic quivers with involution. More precise classification is given when g is a loop Lie algebra, i.e.,when F = C((t)).展开更多
For a truncated quiver algebra over a field of an arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its...For a truncated quiver algebra over a field of an arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles.展开更多
For each finite subgroup G of SLn（C）, we introduce the generalized Cartan matrix AG in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalize...For each finite subgroup G of SLn（C）, we introduce the generalized Cartan matrix AG in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalized Cartan matrices have similar favorable properties such as positive semi- definiteness as in the classical case of affine Cartan matrices. The complete McKay quivers for SL3 （C） are explicitly described and classified based on representation theory.展开更多
In this paper,we show that the McKay quiver of a finite subgroup of a general linear group is a regular covering of the McKay quiver of its intersection with the special linear group.Using this and our results on &quo...In this paper,we show that the McKay quiver of a finite subgroup of a general linear group is a regular covering of the McKay quiver of its intersection with the special linear group.Using this and our results on "returning arrows" in McKay quiver,we give an algorithm to construct the McKay quiver of a finite abelian group.Using this construction,we show how the cone and cylinder of an(n-1)-Auslander absolute n-complete algebra are truncated from the McKay quivers of abelian groups.展开更多
文摘Aloe dichotoma (Quiver tree) occurs in the arid regions of Namaqualand and Bushman land in South Africa, and in arid regions of southern Namibia. The Quiver trees are not only threatened by agricultural expansion, overgrazing, and mining;but also by climate changes and droughts. Previous studies show that Quiver trees are very sensitive to environmental changes, and do not respond well to extreme hot and dry conditions. This study investigates the current status of the Quiver tree within its existing environment, and also assesses the projected future changes of the Quiver tree habitat under different climatic scenarios. It provided evidence regarding the importance of the study to understanding the climate change impacts on the Quiver tree and its geographical response to climate changes.
基金Foundation item:This work is partly supported by NSF(103710036)of Chinakey project(02A024)of provincial Ministry of Foundation of Hunan.
文摘Using the connection between McKay quiver and Loewy matrix, and the properties of characteristic polynomial of Loewy matrix, we give a generalized way to determine the McKay quiver for a finite subgroup of a generalized linear group.
文摘Let A be a basic,connected finite dimensional algebra over an algebraically closed field with finite representation type, α(A) be the maximum of set consisting of numbers of indecomposable summands in the middle term of Auslander Reiten sequences in mod A. In this paper we show that if α(A)=1, then Γ A contains oriented cycles if and only if Γ A contains DT r periodic modules. When α(A)2 we give counterexamples to the assertion.
文摘We study four-dimensional quiver gauge models from F-theory compactified on fourfolds with hyper-K¨ahler structure.Using intersecting complex toric surfaces,we derive a class of N =1 quivers with charged fundamental matter placed on external nodes.The emphasis is on how local Calabi–Yau equations solve the corresponding physical constraints including the anomaly cancelation condition.Concretely,a linear chain of SU(N) groups with flavor symmetries has been constructed using polyvalent toric geometry.
文摘The representations of the Dynkin quivers and the corresponding Euclidean quivers are treated in many books. These notes provide three building blocks for dealing with representations of Dynkin （and Euclidean） quivers. They should be helpful as part of a direct approach to study representations of quivers, and they shed some new light on properties of Dynkin and Euclidean quivers.
基金Supported by National Natural Science Foundation of China(No.11771445).
文摘As generalizations of quivers of type A,Igusa et al.introduced continuous quivers of type A.In this paper,we generalize BGP reflection functors to continuous quivers of type A,and we give another realization of the reflection functor.
文摘We single out a class of translation quivers and prove combinatorially that the translation quivers in this class are coils. These coils form a class of special coils. They are easier to visualize, but still show all the strange behaviour of general coils, and contain quasi-stable tubes as special examples.
基金Supported by Fund of Educational Ministry of China and the Fund of Education Committee of Beijing.
文摘In this paper, we prove that there exists no sectional cycle in a translation quiver under certain conditions. So, we generalize Dautista and Smalφ's corresponding result on AR-quiver of an artin algebra.
文摘We single out a class of translation quivers and prove that the translation quivers in this class are generalized multicoils. These generalized multicoils form a class of special generalized multicoils. They are easier to visualize, but still show all the strange behaviours of generalized multicoils, and contain quasi-stable tubes as special examples.
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 11271318, 11571173） and the Natural Science Foundation of Zhejiang Province （No. LZ13A010001）.
文摘We give sufficient conditions and necessary conditions on duality preservability of Auslander-Reiten quivers of derived categories and cluster categories over hereditary algebras. of generalized path algebras as cleft Meantime, we characterize the condition extensions of path algebras.
文摘We consider stable representations of non-Dynkin quivers with respect to a central charge.These attract a lot of interest in mathematics and physics since they can be identified with so-called BPS states.Another motivation is the work of Dimitrov et al.on the phases of stable representations of the generalized Kronecker quiver.One aim is to explain for general Euclidean and wild quivers the behavior of phases of stable representations well known in some examples.In addition,we study especially the behavior of preinjective,postprojective and regular indecomposable modules.We show that the existence of a stable representation with self-extensions implies the existence of infinitely many stables without self-extensions for rigid central charges.In this case the phases of the stable representations approach one or two limit points.In particular,the phases are not dense in two arcs.The category of representations of acyclic quivers is a special case of rigid Abelian categories which show this behavior for rigid central charges.
基金supported by National Natural Science Foundation of China(Grant No.10671061)theResearch Foundation for Doctor Programme(Grant No.200505042004)
文摘In this paper,we introduce the m-Cartan matrix and observe that some properties of the quadratic form associated to the Cartan matrix of an Euclidean diagram can be generalized to the m-Cartan matrix of a McKay quiver.We also describe the McKay quiver for a finite abelian subgroup of a special linear group.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.10501041,10271113,10601052)
文摘Using the quiver technique we construct a class of non-graded bi-Frobenius algebras.We also classify a class of graded bi-Frobenius algebras via certain equations of structure coefficients.
文摘For a classical group G over a field F together with a finite-order automorphism θ that acts compatibly on F, we describe the fixed point subgroup of θ on G and the eigenspaces of θ on the Lie algebra g in terms of cyclic quivers with involution. More precise classification is given when g is a loop Lie algebra, i.e.,when F = C((t)).
基金the National Natural Science Foundation of China (Grant Nob. 10426014, 10501010 and 10201004)Important Fund of Hubei Provincial Department of Education (Grant No.D200510005)
文摘For a truncated quiver algebra over a field of an arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles.
基金supported by National Natural Science Foundation of China (Grant No. 10728102)National Security Agency (Grant No. MDA 904-97-1-0062)
文摘For each finite subgroup G of SLn（C）, we introduce the generalized Cartan matrix AG in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalized Cartan matrices have similar favorable properties such as positive semi- definiteness as in the classical case of affine Cartan matrices. The complete McKay quivers for SL3 （C） are explicitly described and classified based on representation theory.
基金supported by National Natural Science Foundation of China (Grant No.10971172)
文摘In this paper,we show that the McKay quiver of a finite subgroup of a general linear group is a regular covering of the McKay quiver of its intersection with the special linear group.Using this and our results on "returning arrows" in McKay quiver,we give an algorithm to construct the McKay quiver of a finite abelian group.Using this construction,we show how the cone and cylinder of an(n-1)-Auslander absolute n-complete algebra are truncated from the McKay quivers of abelian groups.
