The first cohomology group of the trivial extension of a monomial algebra

2002/10/18 by Claude Cibils, Cibils, Claude, María Julia Redondo +5
Mathematics · #16E40 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.KT #math.RA #math.RT #msc:16E40

paper · pdf · doi:10.48550/arxiv.math/0210284

Final version to be published in Journal of Algebra and Its Applications (JAA). Small changes from previous version. 13 pages

openalex publication_date 2002/10/18 · arxiv created 2003/06/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a finite--dimensional monomial algebra A we consider the trivial extension TA and provide formulae, depending on the characteristic of the field, for the dimensions of the summands HH₁(A) and \Alt(DA) of the first Hochschild cohomology group HH¹(TA). From these a formula for the dimension of HH¹(TA) can be derived.

Related

• The Lie algebra structure on the first Hochschild cohomology group of a monomial algebra
• The Hochschild cohomology groups under gluing idempotents
• The cohomology of monogenic extensions in the noncommutative setting
• Maximal tori in HH¹ and the fundamental group
• On solvability of the first Hochschild cohomology of a finite-dimensional algebra