On $H^1$ of finite dimensional algebras
Claude Cibils
TL;DR
This paper reviews key results on the first Hochschild cohomology of finite dimensional algebras, providing a dimension formula for certain monomial algebras with acyclic quivers and discussing broader cases.
Contribution
It offers a comprehensive review of Hochschild cohomology results and introduces a dimension formula for monomial algebras with acyclic quivers.
Findings
Dimension formula for monomial algebras with acyclic quivers
Review of Hochschild cohomology results for finite dimensional algebras
Discussion of general monomial case in collaboration with M. Saorin
Abstract
We review results on the first Hochschild cohomology vector space of a finite dimensional algebra, in particular for path algebras modulo a "pre-generated" ideal. In case of a monomial algebra whose quiver has no oriented cycles, a dimension formula is provided. The general monomial case is considered in a paper with M. Saorin.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology