The Lie algebra structure on the first Hochschild cohomology group of a monomial algebra

C. Strametz (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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 (semi-)simplicity, the solvability, the reductivity, the commutativity and the nilpotency are given.

Domaines: Théorie des représentations [math.RT]; Anneaux et algèbres [math.RA]

C. Strametz. The Lie algebra structure on the first Hochschild cohomology group of a monomial algebra. Comptes Rendus. Mathématique, 2002, 334, pp.733-738. ⟨10.1016/S1631-073X(02)02346-4⟩. ⟨hal-00122000⟩