Research Paper#Noncommutative Geometry, Hochschild Homology, DG Categories🔬 ResearchAnalyzed: Jan 3, 2026 06:34
Hochschild Homology of Noncommutative Symmetric Quotient Stacks
Analysis
This paper makes a significant contribution to noncommutative geometry by providing a decomposition theorem for the Hochschild homology of symmetric powers of DG categories, which are interpreted as noncommutative symmetric quotient stacks. The explicit construction of homotopy equivalences is a key strength, allowing for a detailed understanding of the algebraic structures involved, including the Fock space, Hopf algebra, and free lambda-ring. The results are important for understanding the structure of these noncommutative spaces.
Key Takeaways
- •Provides a decomposition theorem for the Hochschild homology of noncommutative symmetric quotient stacks.
- •Uses explicit construction of homotopy equivalences.
- •Reveals connections to Fock spaces, Hopf algebras, and free lambda-rings.
- •Contributes to the understanding of noncommutative geometry.
Reference
“The paper proves an orbifold type decomposition theorem and shows that the total Hochschild homology is isomorphic to a symmetric algebra.”