Related papers: Twisted K-Theory of Lie Groups

We define twisted equivariant K-homology groups using geometric cycles. We compare them with approaches using Kasparov KK-Theory and (twisted) group C*-algebras.

We describe simply connected compact exceptional simple Lie groups in very elementary way. We first construct all simply connected compact exceptional Lie groups G concretely. Next, we find all involutive automorphisms of G, and determine…

We compute the equivariant $K$-theory $K_G^*(G)$ for a simply connected Lie group $G$ (acting on itself by conjugation). We prove that $K_G^*(G)$ is isomorphic to the algebra of Grothendieck differentials on the representation ring. We also…

This note serves as a short and reader-friendly introduction to twisted Brin-Thompson groups, which were recently constructed by Belk and the author to provide a family of simple groups with a variety of interesting properties. Most…

In this paper, we study twisted algebraic $K$-theory from a motivic viewpoint. For a smooth variety $X$ over a field of characteristic zero and an Azumaya algebra $\mathcal{A}$ over $X$, we construct the $\mathcal{A}$-twisted motivic…

We compare different algebraic structures in twisted equivariant K-Theory for proper actions of discrete groups. After the construction of a module structure over untwisted equivariant K-Theory, we prove a completion Theorem of Atiyah-Segal…

Twisted Morava K-theory, along with computational techniques, including a universal coefficient theorem and an Atiyah-Hirzebruch spectral sequence, was introduced by Craig Westerland and the first author. We employ these techniques to…

In this paper, we study a generalization of twisted (groupoid) equivariant $\mathrm{K}$-theory in the sense of Freed-Moore for $\mathbb{Z}_2$-graded $\mathrm{C}^*$-algebras. It is defined by using Fredholm operators on Hilbert modules with…

We show that the twisted group C$^*$-algebra associated with a discrete FC-hypercentral group is simple (resp. has a unique tracial state) if and only if Kleppner's condition is satisfied. This generalizes a result of J. Packer for…

We construct string topology operations in twisted K-theory. We study the examples given by symplectic Grassmannians, computing the twisted K-theory of the loop spaces of quaternionic projective spaces in detail. Via the work of…

In this article we define the twisted product of groups as the generalization of the semidirect product of groups. We will find the necessary and sufficient condition in order that the twisted product of groups to be a group. In particular,…

This paper investigates the $\mathrm{K}$-theory of twisted groupoid $\mathrm{C}^*$-algebras. It is shown that a homotopy of twists on an ample groupoid satisfying the Baum-Connes conjecture with coefficients gives rise to an isomorphism…

We prove the K-theoretic Farrell-Jones conjecture with (twisted) coefficients for CAT(0)-groups.

In this paper, we develop twisted $K$-theory for stacks, where the twisted class is given by an $S^1$-gerbe over the stack. General properties, including the Mayer-Vietoris property, Bott periodicity, and the product structure $K^i_\alpha…

Gives an elementary exposition of the twisted group algebra rep- resentation of simple Clifford algebras

Recent general results on Hamiltonian reductions under polar group actions are applied to study some reductions of the free particle governed by the Laplace-Beltrami operator of a compact, connected, simple Lie group. The reduced systems…

We describe the structure of ``K-approximate subgroups'' of torsion-free nilpotent groups, paying particular attention to Lie groups. Three other works, by Fisher-Katz-Peng, Sanders and Tao, have appeared which independently address related…

We study the structure of abelian extensions of the group $L_qG$ of $q$-differentiable loops (in the Sobolev sense), generalizing from the case of central extension of the smooth loop group. This is motivated by the aim of understanding the…

Let G be a compact, simple, simply connected Lie group. A theorem of Freed-Hopkins-Teleman identifies the level k fusion ring R_k(G) of G with the twisted equivariant K-homology at level k+h, where h is the dual Coxeter number. In this…

Let $\G$ be a locally compact group satisfying some technical requirements and $\wG$ its unitary dual. Using the theory of twisted crossed product $C^*$-algebras, we develop a twisted global quantization for symbols defined on $\G\times\wG$…