NORTHEASTERN UNIVERSITY
MATHEMATICS DEPARTMENT

REPRESENTATION THEORY AND RELATED TOPICS SEMINAR


  Elena Gal
(Tel Aviv)


Symmetric Self-Adjoint Hopf Categories and
a Categorical Heisenberg Double

ABSTRACT: We use the language of higher category theory to define what we call a "symmetric self-adjoint Hopf" (SSH) structure on a semisimple abelian category. SSH categories are the categorical analog of positive self-adjoint Hopf algebras studied by A.Zelevinsky. It follows from his work that for every positive self-adjoint Hopf algebra the Heisenberg double is equipped with a natural action on the algebra. We obtain categorical analogs of the Heisenberg double and its action from the SSH structure on a category in a canonical way. We exhibit the SSH structure on the category of polynomial functors. The categorical Heisenberg double in this case provides a categorification of the infinite dimensional Heisenberg algebra related to the categorification proposed by M. Khovanov.
The preprint is available on arXiv:1406.3973.


September 26, 2014
10:30 - 11:30
511 Lake Hall


For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html  or contact Alex Martsinkovsky alexmart >at< neu >dot< edu