Logarithmic Hennings Invariants for Restricted Quantum sl (2)

Authors

Anna Beliakova, Universität Zürich
Christian Blanchet, Université Paris 7
Alexandra Tebbs, Utah State University

Document Type

Article

Journal/Book Title/Conference

Algebraic & Geometric Topology

Volume

18

Issue

7

Publisher

Mathematical Sciences Publishers

Publication Date

12-11-2018

First Page

4329

Last Page

4358

Abstract

We construct a Hennings-type logarithmic invariant for restricted quantum sl (2) at a 2p^th root of unity. This quantum group U is not quasitriangular and hence not ribbon, but factorizable. The invariant is defined for a pair: a 3–manifold M and a colored link L inside M. The link L is split into two parts colored by central elements and by trace classes, or elements in the 0^th Hochschild homology of U, respectively. The two main ingredients of our construction are the universal invariant of a string link with values in tensor powers of U, and the modified trace introduced by the third author with his collaborators and computed on tensor powers of the regular representation. Our invariant is a colored extension of the logarithmic invariant constructed by Jun Murakami.

Comments

First published in Algebraic & Geometric Topology in Vol. 18 (2018), No. 7, published by Mathematical Sciences Publishers.

Recommended Citation

Beliakova, Anna; Blanchet, Christian; and Tebbs, Alexandra, "Logarithmic Hennings Invariants for Restricted Quantum sl (2)" (2018). Mathematics and Statistics Faculty Publications. Paper 245.
https://digitalcommons.usu.edu/mathsci_facpub/245