The first Hochschild cohomology group of a schurian cluster-tilted algebra
Ibrahim Assem, Maria Julia Redondo
TL;DR
This paper investigates the first Hochschild cohomology group of a schurian cluster-tilted algebra, revealing specific properties and consequences in cases where the algebra is representation-finite or of type ilde{ ext{A}}.
Contribution
It provides new insights into the structure of HH^1(B) for schurian cluster-tilted algebras, especially in representation-finite and type ilde{ ext{A}} cases.
Findings
HH^1(B) has specific properties when B is representation-finite.
The structure of HH^1(B) is characterized for cluster-tilted algebras of type ilde{ ext{A}}.
Several algebraic consequences are derived from the properties of HH^1(B).
Abstract
Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH^1(B) with coefficients in the B-B-bimodule B. We find several consequences when B is representation-finite, and also in the case where B is cluster-tilted of type \tilde{\mathbb{A}}.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons