Hochschild and cyclic (co)homology of the Fomin-Kirillov algebra on 3 generators

2021/12/02 by Estanislao Herscovich, Ziling Li, Herscovich, Estanislao +1
Mathematics · #16E40 #16S37 #16T05 #18G10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2112.01201

openalex publication_date 2021/12/02 · openalex created_date 2021/12/06 · openalex updated_date 2026/07/28

Abstract

The goal of this article is to explicitly compute the Hochschild (co)homology of the Fomin-Kirillov algebra on three generators over a field of characteristic different from 2 and 3. We also obtain the cyclic (co)homology of the Fomin-Kirillov algebra in case the characteristic of the field is zero. Moreover, we compute the algebra structure of the Hochschild cohomology.

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