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

2001/11/06 by C. Strametz, Claudia Strametz, Strametz, C.
Mathematics · #16E40 #16W20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16E40 #msc:16W20

paper · pdf · doi:10.48550/arxiv.math/0111060

22 pages Correction of typing errors

openalex publication_date 2001/11/06 · arxiv created 2001/12/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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