The Lie algebra structure of the first Hochschild cohomology group for monomial algebras

被引：9
|
作者：
Strametz, C [1 ]
机构：
[1] Univ Montpellier 2, Dept Math, Lab GTA UMR 5030, F-34095 Montpellier 5, France
来源：
COMPTES RENDUS MATHEMATIQUE | 2002年 / 334卷 / 09期
关键词：
D O I：
10.1016/S1631-073X(02)02346-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the Lie algebra structure of the first Hochschild cohomology group of a finite dimensional monomial algebra A, in terms of the combinatorics of its quiver, in any characteristic. This allows us also to examine the identity component of the algebraic group of outer automorphisms of A in characteristic zero. Criteria for the solvability, the (semi-) simplicity, the commutativity and the nilpotency are given. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
引用
收藏
页码：733 / 738
页数：6
相关论文
共 50 条
  • [1] THE LIE ALGEBRA STRUCTURE ON THE FIRST HOCHSCHILD COHOMOLOGY GROUP OF A MONOMIAL ALGEBRA
    Strametz, Claudia
    [J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2006, 5 (03) : 245 - 270
  • [2] On the Lie algebra structure of the first Hochschild cohomology of gentle algebras and Brauer graph algebras
    Chaparro, Cristian
    Schroll, Sibylle
    Solotar, Andrea
    [J]. JOURNAL OF ALGEBRA, 2020, 558 : 293 - 326
  • [3] The Lie structure on the Hochschild cohomology of a modular group algebra
    Sanchez-Flores, Selene
    [J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2012, 216 (03) : 718 - 733
  • [4] The first Hochschild cohomology as a Lie algebra
    Rubio y Degrassi, Lleonard
    Schroll, Sibylle
    Solotar, Andrea
    [J]. QUAESTIONES MATHEMATICAE, 2023, 46 (09) : 1955 - 1980
  • [5] Group actions on algebras and the graded Lie structure of Hochschild cohomology
    Shepler, Anne V.
    Witherspoon, Sarah
    [J]. JOURNAL OF ALGEBRA, 2012, 351 (01) : 350 - 381
  • [6] The Lie module structure on the Hochschild cohomology groups of monomial algebras with radical square zero
    Sanchez-Flores, Selene
    [J]. JOURNAL OF ALGEBRA, 2008, 320 (12) : 4249 - 4269
  • [7] On the first Hochschild cohomology group of an algebra
    de la Peña, JA
    Saorín, M
    [J]. MANUSCRIPTA MATHEMATICA, 2001, 104 (04) : 431 - 442
  • [8] On the first Hochschild cohomology group of an algebra
    José Antonio de la Peña
    Manuel Saorín
    [J]. manuscripta mathematica, 2001, 104 : 431 - 442
  • [9] The Hochschild cohomology ring of monomial algebras
    Artenstein, Dalia
    Letz, Janina C.
    Oswald, Amrei
    Solotar, Andrea
    [J]. JOURNAL OF ALGEBRA, 2024, 654 : 108 - 131
  • [10] On the Decomposition of the Hochschild Cohomology Group of a Monomial Algebra Satisfying a Separability Condition
    Itaba, Ayako
    Furuya, Takahiko
    Sanada, Katsunori
    [J]. COMMUNICATIONS IN ALGEBRA, 2015, 43 (06) : 2282 - 2292
12345