Work

Ambidextrous objects and trace functions for nonsemisimple categories

Year: 2011

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1106.4477

Authors: Geer, Nathan, Kujawa, Jonathan, Patureau-Mirand, Bertrand

Institutions: Utah State University, University of Oklahoma, Université Européenne de Bretagne, Université de Bretagne Sud

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Cohomology, Support Varieties, and Representation THeory, Low-Dimensional Topology from a "Super" View Point, Vanishing Quantum Dimensions in Low-dimensional Topology

OpenAlex ID: W2950198532

Cites: 33

Cited by: 8

Related to: 20