The calculus structure of the Hochschild homology/cohomology of preprojective algebras of Dynkin quivers

2007/06/16 by Ching-Hwa Eu, Eu, Ching-Hwa · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.0706.2418

30 pages

openalex publication_date 2007/06/16 · arxiv created 2007/10/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Hochschild homology/cohomology an associative algebra, together with the Connes differential, the contraction map and the Lie derivative, forms the structure of calculus. In this paper we compute explicitely the calculus structure of preprojective algebras of Dynkin quivers over a field of characteristic zero. This also completes the work in math.AG/0502301, where the Batalin-Vilkovisky structure of the Hochschild cohomology of preprojective algebras of non-Dynkin quivers are computed and the calculus can be easily computed from that.

Citations

• The product in the Hochschild cohomology ring of preprojective algebras of Dynkin quivers

Cited by

• Hochschild and cyclic (co)homology of preprojective algebras of quivers of type T
• Calabi-Yau property in derived Koszul calculus

Related

• Hochschild and cyclic (co)homology of preprojective algebras of quivers of type T
• The product in the Hochschild cohomology ring of preprojective algebras of Dynkin quivers
• Hochschild and cyclic homology of preprojective algebras of ADE quivers
• Zeroth Hochschild homology of preprojective algebras over the integers
• Hochschild and cyclic homology of central extensions of preprojective algebras of ADE quivers