4 papers
The Hochschild homology of a noncommutative symmetric quotient stack
Rina Anno, Vladimir Baranovsky, Timothy Logvinenko
We prove an orbifold type decomposition theorem for the Hochschild homology of the symmetric powers of a small DG category . In noncommutative geometry, these can be v…
The Heisenberg algebra of a vector space and Hochschild homology
Ãdám Gyenge, Timothy Logvinenko
We decategorify the Heisenberg 2-category of Gyenge-Koppensteiner-Logvinenko using Hochschild homology. We use this to generalise the Heisenberg algebra action of Grojnowski and Na…
The Heisenberg category of a category
Ãdám Gyenge, Clemens Koppensteiner, Timothy Logvinenko
Starting with a k-linear or DG category admitting a (homotopy) Serre functor, we construct a k-linear or DG 2-category categorifying the Heisenberg algebra of the numerical K-group…
-functors
Rina Anno, Timothy Logvinenko
We propose a new theory of (non-split) P^n-functors. These are F: A -> B for which the adjunction monad RF is a repeated extension of Id_A by powers of an autoequivalence H and thr…