Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modified trace is a symmetrised integral   A modified trace for a finite k-linear pivotal category is a family of linear
forms on endomorphism spaces of projective objects which has cyclicity and
so-called partial trace properties. We show that a non-degenerate modified
trace defines a compatible with duality Calabi-Yau structure on the subcategory
of projective objects. The modified trace provides a meaningful generalisation
of the categorical trace to non-semisimple categories and allows to construct
interesting topological invariants. We prove, that for any finite-dimensional
unimodular pivotal Hopf algebra over a field k, a modified trace is determined
by a symmetric linear form on the Hopf algebra constructed from an integral.
More precisely, we prove that shifting with the pivotal element defines an
isomorphism between the space of right integrals, which is known to be
1-dimensional, and the space of modified traces. This result allows us to
compute modified traces for all simply laced restricted quantum groups at roots
of unity.

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The categories of this paper are: q-alg
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn