Preprint: Symmetric self-adjoint Hopf categories and a categorical Heisenberg double

Preprint: Symmetric self-adjoint Hopf categories and a categorical Heisenberg double

[Adam Gal]

Dear all,

The following preprint is available on the arxiv. We would be really
thankful for any comments or suggestions :)

Symmeric self-adjoint Hopf categories and a categorical Heisenberg double

Adam Gal, Elena Gal

We define what we call a symmetric self-adjoint Hopf structure on a
semisimple abelian category, which is an analog of Zelevinsky's
positive self-adjoint Hopf algebra structure for categories. As
examples we exhibit this structure on the categories of polynomial
functors and equivariant polynomial functors and obtain a categorical
manifestation of Zelevinsky's decomposition theorem involving them. It
follows from the work of Zelevinsky that every positive self-adjoint
Hopf algebra A admits a Fock space action of the Heisenberg double
(A,A). We show that the notion of symmetric self-adjoint Hopf category
leads naturally to the definition of a categorical analog of such an
action and that every symmetric self-adjoint Hopf category admits such
an action

http://arxiv.org/abs/1406.3973

Best regards,
Adam Gal


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