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Superbiderivations of Simple Modular lie superalgebras of Witt Type and Special Type

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代数集刊:英文版 2023年第2期30卷 181-192页

作者： Wei Bai Wende Liu School of Mathematical Sciences Harbin Normal UniversityHarbin 150025China School of Mathematics and Statistics Hainan Normal UniversityHaikou 571158China

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.

关键词： lie superalgebras superbiderivations linear supercommuting maps supercommutative post-lie superalgebra structures

EMBEDDING THEOREM OF FILTERED lie superalgebras

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Acta Mathematica Scientia 2001年第3期21卷 401-411页

作者：张永正沈光宁 Department of Mathematics Northeast Normal University Changchun 130024 China Department of Mathematics East China Normal University Shanghai 200062 China

The homomorphic realization of lie superalgebras and the embedding theorem of filtered lie superalgebras are given and proved.

关键词： lie superalgebras filtered superalgebras associative superalgebra

Classification of Some Nilpotent Class of Leibniz superalgebras

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Acta Mathematica Sinica,English Series 2010年第5期26卷 799-816页

作者： Luisa M.CAMACHO José R.GóMEZ Rosa M.NAVARRO Bakhrom A.OMIROV Dpto. Matemática Aplicada I Universidad de Sevilla Dpto. de Matemáticas Universidad de Extremadura Institute of Mathemátics and Information Technologues Uzbekistan Academy of Science

The aim of this work is to present the description of Leibniz superalgebras up to isomorphism with characteristic sequence （n｜m - 1, 1） and nilindex n ＋ m.

关键词： lie superalgebras Leibniz superalgebras nilindex charasteristic sequence

The Classification of Filiform Leibniz superalgebras of Nilindex n+m

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Acta Mathematica Sinica,English Series 2009年第2期25卷 171-190页

作者： Sh.A.AYUPOV B.A.OMIROV A.Kh.KHUDOYBERDIYEV Institute of Mathematics and Information Technologies of Academy Sciences of Uzbekistan Department of Mathematics National University of Uzbekistan

In this work the classification of filiform Leibniz superalgebras of nilindex n ＋ m, where n and m （m≠0） are dimensions of even and odd parts, respectively, is obtained.

关键词： lie superalgebras Leibniz superalgebras nilpotency characteristic sequence

Modules of the Intermediate Series over Not-finitely Graded lie Algebras W(Г)

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Algebra Colloquium 2021年第2期28卷 319-336页

作者： Yadi Wu Xiaoqing Yue School of Mathematical Sciences Tongji UniversityShanghai 200092China

Let W(Г)be a class of not-finitely graded lie algebras related to generalized Virasoro algebras with basis{L_(α,i),C|α∈Г,i∈Z_(+)},which satisfies relations[L_(α,i),L_(β,j)]=L_(α+β,i+j)+(j-i)L_(α+β,i+j+1)+δ_(α+β,0)δ_(i+j),0α^(3)-α/12 C and[C,L_(α,i)]=0.In this paper,W(Г)-modules of the intermediate series satisfying some conditions are constructed and classified.We also obtain modules of the intermediate series over the related lie superalgebra.

关键词： modules of intermediate series generalized Virasoro algebras not-finitely graded lie algebras lie superalgebras

Simple and Pseudo Quadratic Leibniz superalgebras

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Journal of Applied Mathematics and Physics 2023年第9期11卷 2691-2703页

作者： Mamadou Pouye Bernardin Kpamegan Leonard Todjihoundé Institut de Mathématiques et de Sciences Physiques (IMSP) Porto Novo Bénin Departement de Mathematiques et Informatique Université Cheikh Anta Diop Dakar Sénégal Département de Mathématiques Université Abomey Calavi Cotonou Bénin

Compactness of subspaces of a Z2-graded vector space is introduced and used to study simple Leibniz superalgebras. We introduce left and right super-invariance of bilinear forms over superalgebras. Pseudo-quadratic Leibniz superalgebras are Leibniz superalgebras endowed with a non degenerate, supersymmetric and super-invariant bilinear form. In this paper, we show that every nondegenerate, supersymmetric and super-invariant bilinear form over a Leibniz superalgebra induce a lie superalgebra over the underlying vector space. Then by using double extension extended to Leibniz superalgebras, we study pseudo-quadratic Leibniz superalgebras and the induced lie superalgebras. In particular, we generalize some results on Leibniz algebras to Leibniz superalgebras.

关键词： Leibniz superalgebras lie superalgebras Double Extension Left (Resp. Right) Super-Invariant Bilinear Form