[La structure d'algèbre de Lie du premier groupe de la cohomologie de Hochschild pour des algèbres monomiales]
Nous étudions la structure d'algèbre de Lie du premier groupe de la cohomologie de Hochschild d'une algèbre monomiale de dimension finie Λ, en termes combinatoires de son carquois, en quelconque caractéristique. Cela nous permet aussi d'examiner la composante de l'identité du groupe algébrique des automorphismes extérieurs de Λ en caractéristique zéro. Nous donnons des critères pour la résolubilité, la (semi-)simplicité, la commutativité et la nilpotence.
We study the Lie algebra structure of the first Hochschild cohomology group of a finite dimensional monomial algebra Λ, 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 Λ in characteristic zero. Criteria for the solvability, the (semi-) simplicity, the commutativity and the nilpotency are given.
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@article{CRMATH_2002__334_9_733_0,
author = {Strametz, Claudia},
title = {The {Lie} algebra structure of the first {Hochschild} cohomology group for monomial algebras},
journal = {Comptes Rendus. Math\'ematique},
pages = {733--738},
publisher = {Elsevier},
volume = {334},
number = {9},
year = {2002},
doi = {10.1016/S1631-073X(02)02346-4},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02346-4/}
}
TY - JOUR AU - Strametz, Claudia TI - The Lie algebra structure of the first Hochschild cohomology group for monomial algebras JO - Comptes Rendus. Mathématique PY - 2002 SP - 733 EP - 738 VL - 334 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02346-4/ DO - 10.1016/S1631-073X(02)02346-4 LA - en ID - CRMATH_2002__334_9_733_0 ER -
%0 Journal Article %A Strametz, Claudia %T The Lie algebra structure of the first Hochschild cohomology group for monomial algebras %J Comptes Rendus. Mathématique %D 2002 %P 733-738 %V 334 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02346-4/ %R 10.1016/S1631-073X(02)02346-4 %G en %F CRMATH_2002__334_9_733_0
Strametz, Claudia. The Lie algebra structure of the first Hochschild cohomology group for monomial algebras. Comptes Rendus. Mathématique, Tome 334 (2002) no. 9, pp. 733-738. doi : 10.1016/S1631-073X(02)02346-4. http://www.numdam.org/articles/10.1016/S1631-073X(02)02346-4/
[1] The alternating syzygy behavior of monomial algebras, J. Algebra, Volume 188 (1997) no. 1, pp. 69-89
[2] The first cohomology group of an algebra with coefficients in a bimodule, J. Algebra, Volume 237 (2001) no. 1, pp. 121-141
[3] The cohomology structure of an associative ring, Ann. Math., Volume 78 (1963) no. 2, pp. 267-288
[4] The group of outer automorphisms and the Picard group of an algebra, Algebr. Represent. Theory, Volume 2 (1999) no. 4, pp. 313-330
[5] The automorphism group and the Picard group of a monomial algebra, Comm. Algebra, Volume 27 (1999) no. 2, pp. 857-887
[6] Linear Algebraic Groups, Graduate Texts in Math., 21, Springer, Berlin, 1975
[7] B. Keller, Hochschild cohomology and derived Picard groups, Lecture at the international workshop “Representation Theory around the Channel”, Amiens, France, 31 August–1 September 2001
[8] C. Strametz, The Lie algebra structure on the first Hochschild cohomology group of a monomial algebra, see | arXiv
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