Exponential functors, $R$–matrices and twists
| Autor: | Ulrich Pennig |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
polynomial functors Gerbe Twisted K-theory 01 natural sciences Inner product space Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology 0101 mathematics Twist 55N15 QA twisted $K$–theory Fell bundles Mathematics 55R37 Functor 010102 general mathematics K-Theory and Homology (math.KT) 19L50 55N15 19L50 Characteristic class Exponential function Mathematics - K-Theory and Homology unit spectrum 010307 mathematical physics Geometry and Topology Indecomposable module |
| Zdroj: | Algebr. Geom. Topol. 20, no. 3 (2020), 1279-1324 Ulrich Pennig |
| ISSN: | 1472-2747 |
| Popis: | In this paper we show that each polynomial exponential functor on complex finite-dimensional inner product spaces is defined up to equivalence of monoidal functors by an involutive solution to the Yang-Baxter equation (an involutive $R$-matrix), which determines an extremal character on $S_{\infty}$. These characters are classified by Thoma parameters, and Thoma parameters resulting from polynomial exponential functors are of a special kind. Moreover, we show that each $R$-matrix with Thoma parameters of this kind yield a corresponding polynomial exponential functor. In the second part of the paper we use these functors to construct a higher twist over $SU(n)$ for a localisation of $K$-theory that generalises the one given by the basic gerbe. We compute the indecomposable part of the rational characteristic classes of these twists in terms of the Thoma parameters of their $R$-matrices. 40 pages (fixed a mistake in Sec. 3.2, which does not affect the main result of the paper, Lemma 3.3 has been isolated and moved to an appendix, this agrees (up to minor layout changes) with the version accepted for publication) |
| Databáze: | OpenAIRE |
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