The Real K-Theory of Compact Lie Groups

Abstract

Let $G$ be a compact, connected, and simply-connected Lie group, equipped with a Lie group involution ${\sigma }_G$ and viewed as a $G$-space with the conjugation action. In this paper, we present a description of the ring structure of the (equivariant) $KR$-theory of $(G,{\sigma }_G)$ by drawing on previous results on the module structure of the $KR$-theory and the ring structure of the equivariant $K$-theory.

References in corpus (1)

• Twisted K-theory, old and new

Cited by in corpus (7)

• Real Representations of $C_2$-Graded Groups: The Antilinear Theory
• Equivariant twisted Real $K$-theory of compact Lie groups
• Twisted loop transgression and higher Jandl gerbes over finite groupoids
• Tate blueshift and vanishing for Real oriented cohomology
• Adams operations on classical compact Lie groups
• $KR$-theory of compact Lie groups with group anti-involutions
• The K-theory of the conjugation action