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

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.