A Fourier-Mukai Approach to the K-theory of Compact Lie Groups

TL;DR

This paper introduces a novel proof of the ring structure of the K-theory of compact, simply-connected Lie groups using Fourier-Mukai transforms in twisted K-theory, offering new insights into their algebraic topology.

Contribution

It applies Fourier-Mukai transforms in twisted K-theory to provide a new proof of the K-theory ring structure for compact Lie groups, advancing mathematical understanding.

Findings

New proof of K-theory ring structure for G

Application of Fourier-Mukai transform in twisted K-theory

Enhanced understanding of the algebraic topology of Lie groups

Abstract

Let $G$ be a compact, connected, simply-connected Lie group. We use the Fourier-Mukai transform in twisted $K$-theory to give a new proof of the ring structure of the $K$-theory of $G$.