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
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 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 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.
