A decomposition theorem for the Hochschild homology of symmetric powers of a dg category

2025/11/05 by Nordstrom, Ville
Mathematics · #16E40 14F08 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2511.03269

openalex publication_date 2025/11/05 · openalex created_date 2025/11/07 · openalex updated_date 2026/07/28

Abstract

We prove a conjecture by Belmans, Fu and Krug concerning the Hochschild homology of the symmetric powers of a small dg category \mathscrC. More precisely, we show that these groups decompose into pieces that only depend on the Hochschild homology of the dg category \mathscrC.

Citations

• The Heisenberg algebra of a vector space and Hochschild homology
• Finite group actions on dg categories and Hochschild homology
• Hochschild cohomology of Hilbert schemes of points on surfaces
• The Heisenberg category of a category
• Lefschetz type formulas for dg-categories
• Orbifold Cohomology as Periodic Cyclic Homology

Related

• Finite group actions on dg categories and Hochschild homology
• Hochschild homology invariants of Külshammer type of derived categories
• The global decomposition theorem for Hochschild (co-)homology of singular spaces via the Atiyah-Chern character
• Hochschild cohomology of symmetric groups in low degrees
• Symmetric ring spectra and topological Hochschild homology