Batalin-Vilkovisky algebras and the noncommutative Poincare duality of Koszul Calabi-Yau algebras

2014/06/01 by Xiaojun Chen, Song Yang, Chen, Xiaojun +3 · 2 citations
Mathematics · Physics and Astronomy · #14A22 #16E40 #16S38 #55U30 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA) #math.AG #math.AT #math.RA #msc:14A22 #msc:16E40 #msc:16S38 #msc:55U30

paper · pdf · doi:10.48550/arxiv.1406.0176

Revised and more details added. Guodong Zhou added as the third author. 30 pages

openalex publication_date 2014/06/01 · arxiv created 2015/01/04 · arxiv updated 2015/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a Koszul Calabi-Yau algebra. We show that there exists an isomorphism of Batalin-Vilkovisky algebras between the Hochschild cohomology ring of A and that of its Koszul dual algebra A^!. This confirms (a generalization of) a conjecture of R.~Rouquier.

Citations

• Hochschild (co)homology and Koszul duality
• Graded Calabi Yau algebras of dimension 3
• Calabi-Yau algebras and superpotentials
• The Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra

Cited by

• Poisson structure on bi-graded spaces and Koszul duality, I. The classical case
• Deformation and quantization of the Loday-Quillen-Tsygan isomorphism for Calabi-Yau categories

Related

• Koszul duality and the Hochschild cohomology of Artin-Schelter regular algebras
• Poisson cohomology, Koszul duality, and Batalin-Vilkovisky algebras
• The Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra
• Batalin-Vilkovisky structure on Hochschild cohomology with coefficients in the dual algebra
• Calabi-Yau property in derived Koszul calculus