Let R and S be rings with identity, M be a unitary（R, S）-bimodule and T =（R M0 S）be the upper triangular matrix ring determined by R, S and M. In this paper we prove that under certain conditions a Jordan bideriva...Let R and S be rings with identity, M be a unitary（R, S）-bimodule and T =（R M0 S）be the upper triangular matrix ring determined by R, S and M. In this paper we prove that under certain conditions a Jordan biderivation of an upper triangular matrix ring T is a biderivation of T.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
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
Let Nn（R）be the algebra consisting of all strictly upper triangular n × n matrices over a commutative ring R with the identity.An R-bilinear map φ ：Nn（R）×Nn（R）→ Nn（R）is called a biderivation if it...Let Nn（R）be the algebra consisting of all strictly upper triangular n × n matrices over a commutative ring R with the identity.An R-bilinear map φ ：Nn（R）×Nn（R）→ Nn（R）is called a biderivation if it is a derivation with respect to both arguments.In this paper,we define the notions of central biderivation and extremal biderivation of Nn（R）,and prove that any biderivation of Nn（R）can be decomposed as a sum of an inner biderivation,central biderivation and extremal biderivation for n ≥ 5.展开更多
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
We study conformal biderivations of a Lie conformal algebra.First,we give the definition of a conformal biderivation.Next,we determine the conformal biderivations of loop W(a,b)Lie conformal algebra,loop Virasoro Lie ...We study conformal biderivations of a Lie conformal algebra.First,we give the definition of a conformal biderivation.Next,we determine the conformal biderivations of loop W(a,b)Lie conformal algebra,loop Virasoro Lie conformal algebra,and Virasoro Lie conformal algebra.Especially,all conformal biderivations on Virasoro Lie conformal algebra are inner conformal biderivations.展开更多
In this paper,we mainly study the structure of bi-Jordan n-derivations in triangular rings under conditions of maximal quotient rings and faithful bimodules,respectively.It is shown that every bi-Jordan n-derivation c...In this paper,we mainly study the structure of bi-Jordan n-derivations in triangular rings under conditions of maximal quotient rings and faithful bimodules,respectively.It is shown that every bi-Jordan n-derivation can be decomposed into the sum of an inner biderivation and an extremal biderivation in two different conditions.As by-products,the structures of bi-Jordan n-derivation over upper triangular matrix rings and nest algebras are characterized,respectively,and generalize the known results.展开更多
文摘Let R and S be rings with identity, M be a unitary（R, S）-bimodule and T =（R M0 S）be the upper triangular matrix ring determined by R, S and M. In this paper we prove that under certain conditions a Jordan biderivation of an upper triangular matrix ring T is a biderivation of T.
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.
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).
基金Supported by the National Natural Science Foundation of China(GrantNo.10971117)
文摘Let Nn（R）be the algebra consisting of all strictly upper triangular n × n matrices over a commutative ring R with the identity.An R-bilinear map φ ：Nn（R）×Nn（R）→ Nn（R）is called a biderivation if it is a derivation with respect to both arguments.In this paper,we define the notions of central biderivation and extremal biderivation of Nn（R）,and prove that any biderivation of Nn（R）can be decomposed as a sum of an inner biderivation,central biderivation and extremal biderivation for n ≥ 5.
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.
基金supported by the National Natural Science Foundation of China(Grant Nos.11771069,12071405,11301109)China Postdoctoral Science Foundation(2020M682272)the Natural Science Foundation of Hennan Province(212300410120).
文摘We study conformal biderivations of a Lie conformal algebra.First,we give the definition of a conformal biderivation.Next,we determine the conformal biderivations of loop W(a,b)Lie conformal algebra,loop Virasoro Lie conformal algebra,and Virasoro Lie conformal algebra.Especially,all conformal biderivations on Virasoro Lie conformal algebra are inner conformal biderivations.
基金Supported by the Open Research Fund of Hubei Key Laboratory of Mathematical Sciences(Central China Normal University)the Natural Science Foundation of Anhui Province(Grant No.2008085QA01)the University Natural Science Research Project of Anhui Province(Grant No.KJ2019A0107)。
文摘In this paper,we mainly study the structure of bi-Jordan n-derivations in triangular rings under conditions of maximal quotient rings and faithful bimodules,respectively.It is shown that every bi-Jordan n-derivation can be decomposed into the sum of an inner biderivation and an extremal biderivation in two different conditions.As by-products,the structures of bi-Jordan n-derivation over upper triangular matrix rings and nest algebras are characterized,respectively,and generalize the known results.
