Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ambidextrous objects and trace functions for nonsemisimple categories   We provide a necessary and sufficient condition for a simple object in a
pivotal k-category to be ambidextrous. In turn, these objects imply the
existence of nontrivial trace functions in the category. These functions play
an important role in low-dimensional topology as well as in studying the
category itself. In particular, we prove they exist for factorizable ribbon
Hopf algebras, modular representations of finite groups and their quantum
doubles, complex and modular Lie (super)algebras, the $(1,p)$ minimal model in
conformal field theory, and quantum groups at a root of unity.

20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an