Exponential functors, R-matrices and twists

Pennig, Ulrich ORCID: https://orcid.org/0000-0001-5441-6130 2019. Exponential functors, R-matrices and twists. Algebraic & Geometric Topology 20 , 3. 10.2140/agt.2020.20.1279

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Abstract

This paper contains a natural generalisation of the twist described by the basic gerbe to a higher twist over SU(n) in a localisation of K-theory. Its construction is based on exponential functors on the category of finite-dimensional inner product spaces. It will be shown that each polynomial exponential functor is defined up to equivalence of monoidal functors by an involutive solution to the Yang-Baxter equation (an involutive R-matrix). Likewise, each R-matrix with Thoma parameters (0,(b1,…,bm)) for non-negative integers bi defines a polynomial exponential functor in a natural way. For these twists we will also express the indecomposable part of their rational characteristic classes in terms of their Thoma parameters.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Mathematical Sciences Publishers
ISSN:	1472-2747
Date of First Compliant Deposit:	18 April 2018
Date of Acceptance:	17 April 2018
Last Modified:	15 Nov 2024 13:00
URI:	https://orca.cardiff.ac.uk/id/eprint/110761

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