Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent...Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent Lie group Gk, defined by the nilpotent Lie algebra g/ak, where g is the Lie algebra of G, and ak is an ideal of g. Then, J gives rise to an almost complex structure Jk on Gk. The main conclusion obtained is as follows: if the almost complex structure J of a nilpotent Lie group G is nilpotent, then J can give rise to a left-invariant integrable almost complex structure Jk on the nilpotent Lie group Gk, and Jk is also nilpotent.展开更多
The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.
Let Fq be a finite field. In this paper, a construction of Cartesian au-thentication codes from the normal form of a class of nilpotent matrices over the field Fq is presented. Moreover, assume that the encoding rules...Let Fq be a finite field. In this paper, a construction of Cartesian au-thentication codes from the normal form of a class of nilpotent matrices over the field Fq is presented. Moreover, assume that the encoding rules are chosen according to a uniform probability distribution, the probabilities PI and PS, of a successful im-personation attack and of a successful substitution attack respectively, of these codes are also computed.展开更多
Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）,...Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.展开更多
Let S be an antinegative commutative semiring without zero divisors and Mn（S） be the semiring of all n × n matrices over S. For a linear operator L on Mn（S）, we say that L strongly preserves nilpotent matrice...Let S be an antinegative commutative semiring without zero divisors and Mn（S） be the semiring of all n × n matrices over S. For a linear operator L on Mn（S）, we say that L strongly preserves nilpotent matrices in Mn（S） if for any A ∈ Mn（S）, A is nilpotent if and only if L（A） is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized.展开更多
This article gives characterizations of generalized derivations with skew nilpotent values on noncommutative Lie ideals of a prime ring. The results simultaneously generalize the ones of Herstein, Lee and Carini et al.
In this paper we deal with a cubic near-Hamiltonian system whose unperturbed system is a simple cubic Hamiltonian system having a nilpotent center. We prove that the system can have 5 limit cycles by using bifurcation...In this paper we deal with a cubic near-Hamiltonian system whose unperturbed system is a simple cubic Hamiltonian system having a nilpotent center. We prove that the system can have 5 limit cycles by using bifurcation theory.展开更多
We study the nilpotent structure of generalized semicommutative rings.The new concept of nilpotentα-semicommutative rings is defined and studied.This class of rings is closely related to many well-known concepts incl...We study the nilpotent structure of generalized semicommutative rings.The new concept of nilpotentα-semicommutative rings is defined and studied.This class of rings is closely related to many well-known concepts including semicommutative rings,α-semicommutative rings and weakα-rigid rings.An example is given to show that a nilpotentα-semicommutative ring need not beα-semicommutative.Various properties of this class of rings are investigated.Many known results related to various semicommutative properties of rings are generalized and unified.展开更多
In this paper, we give a complete classification of eight dimensional nilpotent Lie algebras with four-dimensional center by using the method of Skjelbred and Sund.
In this paper,we use the method of representation of Lie group to study a class of nonhomoge- neous convolution operator on the nilpotent Lie group H^M×R^k,and give a criteerion of their hypoellipticity.
We find that a bounded linear operator T on a complex Hilbert space H satisfies the norm relation |||T|na|| =2q, for any vector a in H such that q≤(||Ta||-4-1||Ta||2)≤1.A partial converse to Theorem 1 by Haagerup an...We find that a bounded linear operator T on a complex Hilbert space H satisfies the norm relation |||T|na|| =2q, for any vector a in H such that q≤(||Ta||-4-1||Ta||2)≤1.A partial converse to Theorem 1 by Haagerup and Harpe in [1] is suggested. We establish an upper bound for the numerical radius of nilpotent operators.展开更多
In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems ab...In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems about nilpotent subgroup.展开更多
A group G is said to an FN<sub>c</sub>-group if the （c+1）th term γ<sub>c+1</sub>G of its lower central series is finite（or equivalently if it is finite-by-nilpotent of class≤c）.A group G ...A group G is said to an FN<sub>c</sub>-group if the （c+1）th term γ<sub>c+1</sub>G of its lower central series is finite（or equivalently if it is finite-by-nilpotent of class≤c）.A group G is called a JNFN<sub>c</sub>-group if all itsproper quotients are FN<sub>c</sub>-groupe but G itself is not.The structure of JNFA-groups（JNFN<sub>c</sub>-groupswith c=1） has been described in a joint work of D.J.S Robinson and the author（see J.Algebra,（2）118（1988）,346～368）.Now we consider JNFN<sub>c</sub>-groups with non-trivial Fitting subgroup forarbitrary c and give a complete description of groups of this type.展开更多
An n × n complex sign pattern （ray pattern） S is said to be spectrally arbitrary if for every monic nth degree polynomial f（λ） with coefficients from C, there is a complex matrix in the complex sign pattern ...An n × n complex sign pattern （ray pattern） S is said to be spectrally arbitrary if for every monic nth degree polynomial f（λ） with coefficients from C, there is a complex matrix in the complex sign pattern class （ray pattern class） of 3 such that its characteristic polynomial is f（λ）. We derive the Nilpotent-Centralizer methods for spectrally arbitrary complex sign patterns and ray patterns, respectively. We find that the Nilpotent-Centralizer methods for three kinds of patterns （sign pattern, complex sign pattern, ray pattern） are the same in form.展开更多
Let G be a finite group.We denote byν(G)the probability that two randomly chosen elements of G generate a nilpotent subgroup.In this paper,we characterize the structure of finite groups G with lower bounds\({1\over p...Let G be a finite group.We denote byν(G)the probability that two randomly chosen elements of G generate a nilpotent subgroup.In this paper,we characterize the structure of finite groups G with lower bounds\({1\over p},\,{{p^{2}+8}\over{9p^{2}}}\)and\({p+3}\over{4p}\)onν(G),where p is a prime divisor of∣G∣.展开更多
An exceptional cycle in a triangulated category with Serre functor is a general-ization of a spherical object and a fractional Calabi-Yau object.We consider the bounded derived categories D^(b)(T_(n))and D^(b)(T_(∞))...An exceptional cycle in a triangulated category with Serre functor is a general-ization of a spherical object and a fractional Calabi-Yau object.We consider the bounded derived categories D^(b)(T_(n))and D^(b)(T_(∞)),and the cluster categories C_(Tn) and C_(T∞),where T_(n) and T_(∞) are the hereditary abelian categories of nilpotent finite-dimensional represen-tations of the quivers A_(n-1) and A_(∞)^(∞),respectively,with all arrows oriented in the same direction.There is a unique exceptional cycle in D^(b)(T_(n))and in C_(T∞),up to the equivalence relation ≈,and the actions of the auto-equivalences induced by these exceptional cycles are explicitly given.We point out that there are no exceptional cycles in C_(Tn) or in D^(b)(T_(∞)).We also show that the possible length of exceptional cycles in a Calabi-Yau category T is 1 or 2;if in addition T is homotopy-like and T■D^(b)(k),then the possible length is only 1 and any exceptional l-cycle is at the mouth.展开更多
We study the quasi-admissibility and raisability of some nilpotent orbits of a covering group.In particular,we determine the degree of the cover such that a given split nilpotent orbit is quasi-admissible and non-rais...We study the quasi-admissibility and raisability of some nilpotent orbits of a covering group.In particular,we determine the degree of the cover such that a given split nilpotent orbit is quasi-admissible and non-raisable.The speculated wavefront sets of theta representations are also computed explicitly and are shown to be quasi-admissible and non-raisable.Lastly,we determine the leading coefficients in the Harish-Chandra character expansion of the theta representations of covers of the general linear groups.展开更多
文摘Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent Lie group Gk, defined by the nilpotent Lie algebra g/ak, where g is the Lie algebra of G, and ak is an ideal of g. Then, J gives rise to an almost complex structure Jk on Gk. The main conclusion obtained is as follows: if the almost complex structure J of a nilpotent Lie group G is nilpotent, then J can give rise to a left-invariant integrable almost complex structure Jk on the nilpotent Lie group Gk, and Jk is also nilpotent.
基金supported by NSFC (10871192)NSF of Hebei Province (A2010000194)
文摘The notions of the nilpotent and the strong-nilpotent Leibniz 3-algebras are defined. And the three dimensional two-step nilpotent, strong-nilpotent Leibniz 3-algebras are classified.
文摘Let Fq be a finite field. In this paper, a construction of Cartesian au-thentication codes from the normal form of a class of nilpotent matrices over the field Fq is presented. Moreover, assume that the encoding rules are chosen according to a uniform probability distribution, the probabilities PI and PS, of a successful im-personation attack and of a successful substitution attack respectively, of these codes are also computed.
基金The NSF(11371124)of Chinathe NSF(F2015402033)of Hebei Provincethe Doctoral Special Foundation(20120066)of Hebei University of Engineering
文摘Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.
文摘Let S be an antinegative commutative semiring without zero divisors and Mn（S） be the semiring of all n × n matrices over S. For a linear operator L on Mn（S）, we say that L strongly preserves nilpotent matrices in Mn（S） if for any A ∈ Mn（S）, A is nilpotent if and only if L（A） is nilpotent. In this paper, the linear operators that strongly preserve nilpotent matrices over S are characterized.
文摘This article gives characterizations of generalized derivations with skew nilpotent values on noncommutative Lie ideals of a prime ring. The results simultaneously generalize the ones of Herstein, Lee and Carini et al.
文摘In this paper we deal with a cubic near-Hamiltonian system whose unperturbed system is a simple cubic Hamiltonian system having a nilpotent center. We prove that the system can have 5 limit cycles by using bifurcation theory.
基金Supported by the Natural Science Foundation of Jiangsu Province(Grant No.BK20181406)the National Natural Science Foundation of China(Grant No.12161049)。
文摘We study the nilpotent structure of generalized semicommutative rings.The new concept of nilpotentα-semicommutative rings is defined and studied.This class of rings is closely related to many well-known concepts including semicommutative rings,α-semicommutative rings and weakα-rigid rings.An example is given to show that a nilpotentα-semicommutative ring need not beα-semicommutative.Various properties of this class of rings are investigated.Many known results related to various semicommutative properties of rings are generalized and unified.
基金Supported by the National Natural Science Foundation of China (Grant No.J1103110)
文摘In this paper, we give a complete classification of eight dimensional nilpotent Lie algebras with four-dimensional center by using the method of Skjelbred and Sund.
文摘In this paper,we use the method of representation of Lie group to study a class of nonhomoge- neous convolution operator on the nilpotent Lie group H^M×R^k,and give a criteerion of their hypoellipticity.
文摘We find that a bounded linear operator T on a complex Hilbert space H satisfies the norm relation |||T|na|| =2q, for any vector a in H such that q≤(||Ta||-4-1||Ta||2)≤1.A partial converse to Theorem 1 by Haagerup and Harpe in [1] is suggested. We establish an upper bound for the numerical radius of nilpotent operators.
文摘In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems about nilpotent subgroup.
文摘A group G is said to an FN<sub>c</sub>-group if the （c+1）th term γ<sub>c+1</sub>G of its lower central series is finite（or equivalently if it is finite-by-nilpotent of class≤c）.A group G is called a JNFN<sub>c</sub>-group if all itsproper quotients are FN<sub>c</sub>-groupe but G itself is not.The structure of JNFA-groups（JNFN<sub>c</sub>-groupswith c=1） has been described in a joint work of D.J.S Robinson and the author（see J.Algebra,（2）118（1988）,346～368）.Now we consider JNFN<sub>c</sub>-groups with non-trivial Fitting subgroup forarbitrary c and give a complete description of groups of this type.
基金National Natural Science Foundation of China(Grant No.11071227)Shanxi Scholarship Councilof China(Grant No.12-070)
文摘An n × n complex sign pattern （ray pattern） S is said to be spectrally arbitrary if for every monic nth degree polynomial f（λ） with coefficients from C, there is a complex matrix in the complex sign pattern class （ray pattern class） of 3 such that its characteristic polynomial is f（λ）. We derive the Nilpotent-Centralizer methods for spectrally arbitrary complex sign patterns and ray patterns, respectively. We find that the Nilpotent-Centralizer methods for three kinds of patterns （sign pattern, complex sign pattern, ray pattern） are the same in form.
基金Supported by NSF of China(Grant No.12061011)NSF of Guangxi(Grant Nos.2020GXNSFDA238014,2021GXNSFAA220105)。
文摘Let G be a finite group.We denote byν(G)the probability that two randomly chosen elements of G generate a nilpotent subgroup.In this paper,we characterize the structure of finite groups G with lower bounds\({1\over p},\,{{p^{2}+8}\over{9p^{2}}}\)and\({p+3}\over{4p}\)onν(G),where p is a prime divisor of∣G∣.
基金Supported by National Natural Science Foundation of China(Grant Nos.12131015,12401047)Natural Science Research of the Jiangsu Higher Education Institutions of China(Grant No.24KJB110022)Natural Science Foundation of Shanghai(Grant No.23ZR1435100).
文摘An exceptional cycle in a triangulated category with Serre functor is a general-ization of a spherical object and a fractional Calabi-Yau object.We consider the bounded derived categories D^(b)(T_(n))and D^(b)(T_(∞)),and the cluster categories C_(Tn) and C_(T∞),where T_(n) and T_(∞) are the hereditary abelian categories of nilpotent finite-dimensional represen-tations of the quivers A_(n-1) and A_(∞)^(∞),respectively,with all arrows oriented in the same direction.There is a unique exceptional cycle in D^(b)(T_(n))and in C_(T∞),up to the equivalence relation ≈,and the actions of the auto-equivalences induced by these exceptional cycles are explicitly given.We point out that there are no exceptional cycles in C_(Tn) or in D^(b)(T_(∞)).We also show that the possible length of exceptional cycles in a Calabi-Yau category T is 1 or 2;if in addition T is homotopy-like and T■D^(b)(k),then the possible length is only 1 and any exceptional l-cycle is at the mouth.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1005300)National Natural Science Foundation of China(Grant No.12171422)+1 种基金supported by U.S.National Science Foundation(Grant Nos.DMS-1702218 and DMS-1848058)supported by the NSTC Funds(Grant Nos.108-2115-M-033-004-MY3 and 111-2115-M-033-001-MY3).
文摘We study the quasi-admissibility and raisability of some nilpotent orbits of a covering group.In particular,we determine the degree of the cover such that a given split nilpotent orbit is quasi-admissible and non-raisable.The speculated wavefront sets of theta representations are also computed explicitly and are shown to be quasi-admissible and non-raisable.Lastly,we determine the leading coefficients in the Harish-Chandra character expansion of the theta representations of covers of the general linear groups.
