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书名 | 李超代数及相关的代数结构(英文版) |
分类 | 科学技术-自然科学-数学 |
作者 | 张润萱 |
出版社 | 吉林大学出版社 |
下载 | ![]() |
简介 | 内容推荐 李超代数在李理论、微分几何及数学物理等领域起着重要的作用。张润萱著的《李超代数及相关的代数结构(英文版)》是著者今年来研究李超代数及相关的代数结构的最新研究成果,主要包括李超代数的广义导子超代数、左对称超代数及w-李代数。本书结构安排如下:第一部分(第一至四章)回顾李超代数、左对称超代数、Hom-型超代数以及w-李代数的背景和基本概念;第二部分(第五至九章)是本专著的核心,研究内容包括:1.李超代数的广义导子和拟导子超代数;2.低维左对称超代数的分类;3.单李超代数上的相容左对称超代数结构;4.左对称超双代数的相关性质,并且诱导出与李超代数上的分次经典杨-巴斯特方程类似的左对称超代数上的方程;5.通过Hom-型Novikov超代数的仿射化构造了一些无限维Hom型李超代数。第三部分(第十至十二章)研究一类比较新的代数结构:w-李代数,包括低维分类和导子、自同构以及表示理论的研究。 目录 Part I Preliminaries on Lie Superalgebas and Related Algebras 1 Lie Superalgebras 1.1 Graded vector spaces and superalgebras 1.2 Lie superalgebras 2 Left-symmetric Superalgebras 2.1 Background 2.2 Constructions of left-symmetric superalgebras 2.3 The classification problem 3 Hom-type Superalgebras 3.1 Background 3.2 Hom-type superalgebras 4 co-Lie Algebras 4.1 Background 4.2 Basic concepts Part II Lie Superalgebras and Left-symmetric Superalgebras 5 Generalized Derivations of Lie Superalgebras 5.1 Generalized derivations and quasiderivations 5.2 Lie superalgebra cj with QDer(g) = gl(g) 5.3 Quasiderivations of Lie superalgebras 6 Low-dimensional Left-symmetric Superalgebras 6.1 Two-dimensional left-symmetric saperalgebras 6.1.1 Left-symmetric superalgebras on (B1) 6.1.2 Left-symmetric superalgebras on (B2) 6.1.3 Left-symmetric superalgebras on (B3) 6.2 Three-dimensional left-symmetric superalgebras with one-dimensional even part 6.2.1 Left-symmetric superalgebras on (Ci) 6.2.2 Left-symmetric superalgebras on (C2)λ 6.2.3 Left-symmetric superalgebras on (C3) 6.2.4 Left-symmetric superalgebras on (C4) 6.2.5 Left-symmetric superalgebras on (C5) 6.2.6 Left-symmetric superalgebras on (Qi) 6.3 Three-dimensional left-symmetric superalgebras with two-dimensional even part 6.4 An application: graded CYBE in Lie superalgebras 7 Left-symmetric Superalgebras on Simple Lie Superalgebras. 7.1 General results 7.2 1-cocycles and left-symmetric superalgebras 7.2.1 Bijective 1-cocycles and left-symmetric superalgebras 7.2.2 Equivalence and quasi-equivalence 7.2.3 Evaluation mapping 7.3 Left-symmetric superalgebras on sl(n|l) 7.4 Left-symmetric superalgebras on sl(2|l) 7.4.1 Some Lemmas 7.4.2 Bijective evaluation mappings and left-symmetric superalgebras associated with the module K(λ1) K(λ1') 7.4.3 Bijective evaluation mappings and left-symmetric superalgebras associated with the module K(λ1)(2) 7.4.4 Bijective evaluation mappings and left-symmetric superalgebras associated with K(λ2) 7.5 Left-symmetric superalgebras on SI(n + 1 |n) 7.6 Left-symmetric superalgebras on W(n) 8 Left-symmetric Bisuperalgebras and the Graded s-Equation 8.1 Matched pairs and graded phase spaces of Lie superalgebras 8.2 Bimodules and matched pairs of left-symmetric superalgebras 8.3 Left-symmetric bisuperalgebras 8.4 Coboundary left-symmetric bisuperalgebras 8.5 The Graded 5-equation and S-operators of left-symmetric superalgebras 9 Infinite-dimensional Hom-Lie Superalgebras 9.1 Infinite-dimensional Hom-Lie superalgebras 9.1.1 Construction of Hom-Lie superalgebras from Hom-BN superalgebras 9.1.2 Construction of Hom-Lie superalgebras from Hom-Novikov superalgebras 9.2 Central extensions of Hom-Lie superalgebras 9.2.1 Central extensions of Hom-Lie Superalgebras 9.2.2 Bilinear forms with certain invariance conditions on Hom-BN superalgebras 9.2.3 Bilinear forms with certain invariance conditions on Hom-Novikov superalgebras Part III ω-Lie Algebras 10 Three-dimensional co-Lie Algebras 10.1 Main results 10.2 Ranks 0 and 1 10.3 Rank 2 10.4 Rank 3 10.5 Remarks 11 Four-dimensional and Simple co-Lie Algebras 11.1 Main results and a sketch of proof 11.2 Proof of Theorem 11.1 11.2.1 ω-Lie algebras containing L1 11.2.2 ω-Lie algebras containing L2 11.2.4 ω-Lie algebras containing B 11.2.5 ω-Lie algebras containing Ca 11.3 Simple co-Lie algebras and more discussions 12 Derivations, Automorphisms and Representations 12.1 Three-dimensional derivations 12.2 Three-dimensional automorphisms 12.3 Four-dimens |
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