A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgeb...A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.展开更多
In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obta...In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obtain the concrete characterizations of all nonadditive skew(anti-)commuting maps on some operator algebras.展开更多
The existence of common fixed points and invariant approximations for pointwise R- subweakly commuting and compatible maps is established. Our results unify and generalize various known results to a more general class...The existence of common fixed points and invariant approximations for pointwise R- subweakly commuting and compatible maps is established. Our results unify and generalize various known results to a more general class of noncommuting mappings.展开更多
Let N be a nest on a Banach space X, and AlgN be the associated nest algebra. It is shown that, if there exists a non-trivial element N in N which is complemented in X and dim N ≠ 1, then every additive biderivation ...Let N be a nest on a Banach space X, and AlgN be the associated nest algebra. It is shown that, if there exists a non-trivial element N in N which is complemented in X and dim N ≠ 1, then every additive biderivation from AlgN into itself is an inner biderivation. Based on this result, we give characterizations of centralizing （commuting） maps, cocentraliz-ing derivations, and cocommuting generalized derivations on nest algebras.展开更多
In the present paper, we show that there exists a unique common fixed point for four self maps in a fuzzy metric space where two of the maps are reciprocally continuous and the other two maps are z-asymptotically comm...In the present paper, we show that there exists a unique common fixed point for four self maps in a fuzzy metric space where two of the maps are reciprocally continuous and the other two maps are z-asymptotically commuting.展开更多
Let R be an arbitrary commutative ring with identity, and let Nn（R） be the set consisting of all n × n strictly upper triangular matrices over R. In this paper, we give an explicit description of the maps（with...Let R be an arbitrary commutative ring with identity, and let Nn（R） be the set consisting of all n × n strictly upper triangular matrices over R. In this paper, we give an explicit description of the maps（without linearity or additivity assumption） φ ： Nn（R） → Nn（R）satisfying φ（xy） = φ（x）y ＋ xφ（y）. As a consequence, additive derivations and derivations of Nn（R） are also described.展开更多
Our purpose is to determine skew-symmetric biderivations Bider s(L,V)and commuting linear maps Com(L,V)on a multiplicative Hom-Lie algebra(L,α)having their ranges in an(L,α)-module(V,ρ,β),which are both closely re...Our purpose is to determine skew-symmetric biderivations Bider s(L,V)and commuting linear maps Com(L,V)on a multiplicative Hom-Lie algebra(L,α)having their ranges in an(L,α)-module(V,ρ,β),which are both closely related to Cent(L,V),the centroid of(L,α)on(V,ρ,β).We give the relationship between biderivations and commuting linear maps on a regular Hom-Lie algebra and those on the related Lie algebra.Under appropriate assumptions,we also prove that everyδin Bider_(s)(L,V)is of the formδ(x,y)=β^(−1)γ([x,y])for someγ∈Cent(L,V),and Com(L,V)coincides with Cent(L,V).Besides,we give the algorithms for describing Bider s(L,V)and Com(L,V).展开更多
In lhis paper we draw some coincidence and common fixed point theorems fornonlinear hybrid contraction mappings on probabilistic metric spaces with a convexstructure.
In this paper we study the properties of the set consisting of all fixed points of a Scott continuous self-map between domains. All the results give an answer to an open problem posed by Lawson and Mislove in 1990.
Let F be a field with charF ≠ 2 and ｜F｜ 〉 9, and let B2n（F） be the standard Borel subgroup of the unitary group U2n（F） over F. For n ≥ 3, we obtain a complete description of all bijective maps preserving comm...Let F be a field with charF ≠ 2 and ｜F｜ 〉 9, and let B2n（F） be the standard Borel subgroup of the unitary group U2n（F） over F. For n ≥ 3, we obtain a complete description of all bijective maps preserving commutators on B2n （F）.展开更多
Abstract Let F be a field, and let G be the standard Borel subgroup of the symplectie group Sp（2m, F）. In this paper, we characterize the bijective maps φ： G -- G satisfying φ[x, y] = [φ（x）, φ（y）].
On Hom-Lie algebras and superalgebras,we introduce the notions of biderivations and linear commuting maps,and compute them for some typical Hom-Lie algebras and superalgebras,including the q-deformed W(2,2)algebra,the...On Hom-Lie algebras and superalgebras,we introduce the notions of biderivations and linear commuting maps,and compute them for some typical Hom-Lie algebras and superalgebras,including the q-deformed W(2,2)algebra,the q-deformed Witt algebra and superalgebra.展开更多
基金Supported by the National Natural Science Foundation of China（Ill01084） Supported by the Fujian Province Natural Science Foundation of China
文摘A map φ on a Lie algebra g is called to be commuting if [φ(x), x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.
基金supported by the National Natural Science Foundation of China (Nos.12171290,12301152)the Natural Science Foundation of Shanxi Province (No.202203021222018)。
文摘In this paper,we first give the general forms of skew commuting maps and skew anti-commuting maps by the Peirce decomposition on a unital ring with a nontrivial idempotent,respectively,and then,as applications,we obtain the concrete characterizations of all nonadditive skew(anti-)commuting maps on some operator algebras.
文摘The existence of common fixed points and invariant approximations for pointwise R- subweakly commuting and compatible maps is established. Our results unify and generalize various known results to a more general class of noncommuting mappings.
基金Supported by the National Natural Science Foundation of China(Grant No.11101250)Youth Foundation ofShanxi Province(Grant No.2012021004)
文摘Let N be a nest on a Banach space X, and AlgN be the associated nest algebra. It is shown that, if there exists a non-trivial element N in N which is complemented in X and dim N ≠ 1, then every additive biderivation from AlgN into itself is an inner biderivation. Based on this result, we give characterizations of centralizing （commuting） maps, cocentraliz-ing derivations, and cocommuting generalized derivations on nest algebras.
文摘In the present paper, we show that there exists a unique common fixed point for four self maps in a fuzzy metric space where two of the maps are reciprocally continuous and the other two maps are z-asymptotically commuting.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117134311426121)+1 种基金the Science Foundation of Jiangxi University of Science and Technology(Grant Nos.NSFJ2014–K12NSFJ2015–G24)
文摘Let R be an arbitrary commutative ring with identity, and let Nn（R） be the set consisting of all n × n strictly upper triangular matrices over R. In this paper, we give an explicit description of the maps（without linearity or additivity assumption） φ ： Nn（R） → Nn（R）satisfying φ（xy） = φ（x）y ＋ xφ（y）. As a consequence, additive derivations and derivations of Nn（R） are also described.
基金supported by NSF of Jilin Province(YDZJ202301ZYTS381)NSF of China(11901057)+5 种基金SRF of Jilin Provincial Education Department(JJKH20220821KJ)NSF of Changchun Normal Universitysupported by NSF of China(11801066,11771410)and CSC of China(202106625001)supported by NSF of Jilin Province(YDZJ202201ZYTS589)NSF of China(12271085,12071405)the Fundamental Research Funds for the Central Universities.
文摘Our purpose is to determine skew-symmetric biderivations Bider s(L,V)and commuting linear maps Com(L,V)on a multiplicative Hom-Lie algebra(L,α)having their ranges in an(L,α)-module(V,ρ,β),which are both closely related to Cent(L,V),the centroid of(L,α)on(V,ρ,β).We give the relationship between biderivations and commuting linear maps on a regular Hom-Lie algebra and those on the related Lie algebra.Under appropriate assumptions,we also prove that everyδin Bider_(s)(L,V)is of the formδ(x,y)=β^(−1)γ([x,y])for someγ∈Cent(L,V),and Com(L,V)coincides with Cent(L,V).Besides,we give the algorithms for describing Bider s(L,V)and Com(L,V).
文摘In lhis paper we draw some coincidence and common fixed point theorems fornonlinear hybrid contraction mappings on probabilistic metric spaces with a convexstructure.
基金the National Natural Science Foundation of China (Grant. No. 10071053) the SFEM of China and the Project of "Excellent Scholars Crossing Centuries" of the Education Ministry of China.
文摘In this paper we study the properties of the set consisting of all fixed points of a Scott continuous self-map between domains. All the results give an answer to an open problem posed by Lawson and Mislove in 1990.
文摘Let F be a field with charF ≠ 2 and ｜F｜ 〉 9, and let B2n（F） be the standard Borel subgroup of the unitary group U2n（F） over F. For n ≥ 3, we obtain a complete description of all bijective maps preserving commutators on B2n （F）.
文摘Abstract Let F be a field, and let G be the standard Borel subgroup of the symplectie group Sp（2m, F）. In this paper, we characterize the bijective maps φ： G -- G satisfying φ[x, y] = [φ（x）, φ（y）].
基金Supported by National Natural Science Foundation grants of China(Grant No.11301109)。
文摘On Hom-Lie algebras and superalgebras,we introduce the notions of biderivations and linear commuting maps,and compute them for some typical Hom-Lie algebras and superalgebras,including the q-deformed W(2,2)algebra,the q-deformed Witt algebra and superalgebra.
