查看更多>>摘要：Let L be a simple modular Lie superealgebra of Witt type or special type over an algebraically closed field of characteristic p＞2.In this paper,all the super-biderivations of L are studied.By means of weight space decompositions with respect to a suitable torus and the standard Z-grading structures of L,we show that the super-symmetric superbiderivations of L are zero.Generalizing a result on the skewsymmetric biderivation of Lie algebras to the super case,we find that all the superbiderivations of L are inner.As applications,the linear supercommuting maps and the supercommutative post-Lie superalgebra structures on L are described.
查看更多>>摘要：The new concept"derimorphism"generalizing both derivation and homomor-phism is defined.When a derimorphism is invertible,its inverse is a Rota-Baxter operator.The general theory of derimorphism is established.The classification of all derimorphisms over an associative unital algebra is obtained.Contrary to the nonexistence of nontriv-ial positive derivations,it is shown that nontrivial positive derimorphisms do exist over any pair of opposite orderings over R[x],the lattice-ordered full matrix algebra and upper triangular matrix algebra over a totally ordered field.
查看更多>>摘要：Let Aq=k(x,y)/(x2,xy+qyx,y2)over a field k.We give a clear character-ization of the Batalin-Vilkovisky algebraic structure on Hochschild cohomology of Aq for any q≠0,and the Gerstenhaber algebraic structure on Hochschild cohomology of Aq for q=0.
查看更多>>摘要：Higher differential objects are investigated and used for addressing three gen-eral problems.Torsionless differential modules over path algebras are characterized.The adjoint triples between triangulated categories,involving derived categories and singularity categories,are allowed to be constructed from those between the abelian categories C and C[ε]n.The partial silting properties between an abelian category C and C[ε]n are trans-ferred,and if moreover,C is Frobenius,the partial silting objects of the stable monomor-phism categories of C[ε]n are constructed from those of C.
查看更多>>摘要：Let R=K[x1,…,xn]be the polynomial ring in n variables over a field K and I be a matroidal ideal of R.We show that I is sequentially Cohen-Macaulay if and only if the Alexander dual IV has linear quotients.As a consequence,I is sequentially Cohen-Macaulay if and only if I is shellable.
查看更多>>摘要：Let(H,αH,βH,ψH,ωH,SH)be a BiHom-Hopf algebra and(A,αA,βA)be an(H,αH,βH,ψH,ωH)-BiHom-bimodule algebra,where the maps αH,βH,ψH,ωH,αA,βA are bijective.We first prove the Maschke-type theorem for the BiHom-L-R smash product over a finite-dimensional semisimple BiHom-Hopf algebra.Next we give a Morita context between the BiHom-subalgebra AbiH and the BiHom-L-R smash product A#H.
查看更多>>摘要：Let R be a finite Lie conformal algebra.We investigate the conformal deriva-tion algebra CDer(R),conformal triple derivation algebra CTDer(R)and generalized con-formal triple derivation algebra GCTDer(R),focusing mainly on the connections among these derivation algebras.We also give a complete classification of(generalized)con-formal triple derivation algebras on all finite simple Lie conformal algebras.In partic-ular,CTDer(R)=CDer(R),where R is a finite simple Lie conformal algebra.But for GCDer(R),we obtain a conclusion that is closely related to CDer(R).Finally,we introduce the definition of a triple homomorphism of Lie conformal algebras.Triple homomorphisms of all finite simple Lie conformal algebras are also characterized.
查看更多>>摘要：In this paper,we describe multiplicative derivations on the set of all rank-s matrices of Mn(K)over a field K with a relatively small integer s.Concretely,for fixed integers n,s satisfying 1 ≤ s ≤ n/2 and n ≥ 2,we prove that if a map δ:Mn(K)→ Mn(K)satisfies δ(xy)=δ(x)y+xδ(y)for any two rank-s matrices x,y ∈ Mn(K),then there exists a derivation D of Mn(K)such that δ(x)=D(x)for each rank-k matrix x ∈ Mn(K)with 0 ≤ k ≤ s.As an application,we prove that a multiplicative derivation on a special subset of Mn(K)must be a derivation.
查看更多>>摘要：A finite p-group G is called an At-group if t is the minimal non-negative integer such that all subgroups of index pt of G are abelian.The finite p-groups G with H'=G'for all A2-subgroups H of G are classified completely in this paper.As an application,a problem proposed by Berkovich is solved.
查看更多>>摘要：Let V be a faithful G-module for a finite group G and let p be a prime dividing|G|.An orbit vG for the action of G on V is regular if|vG|=|G:CG(v)|=|G|,and is p-regular if|vG |p=|G:CG(V)|p=|G|p.In this note,we study two questions,one by the authors and one by Isaacs,related to the p-regular orbits and regular orbits of the linear group actions.
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