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

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

2001-11-06

arxiv.org/abs/math/0111060v2

Mathematics

Representation Theory

22 pages Correction of typing errors

Scientific paper

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.

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