Algebraic and Arithmetic Geometry Seminar
# The Heisenberg category of a category

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Aula Magna (Department of Mathematics)
### Aula Magna

#### Department of Mathematics

Description

The Heisenberg algebra associated with a lattice is a much-investigated object originating in quantum theory. Khovanov introduced

recently a categorification of the infinite Heisenberg algebra

associated with the free boson or, equivalently, a rank 1 lattice,

using a graphical construction involving planar diagrams. We extend

Khovanov’s graphical construction to derived categories of smooth and

projective varieties or, more generally, to categories having a Serre

functor. In our case, the underlying lattice will be the (numerical)

Grothendieck group of the category. We also obtain a 2-representation

of our Heisenberg category on a categorical analogue of the Fock

space. Joint work with Clemens Koppensteiner and Timothy Logvinenko.