Related papers: The Verlinde algebra is twisted equivariant K-theo…

Let S be a finitely generated subsemigroup of Z^2. We derive a general formula for the K-theory of the left regular C*-algebra for S.

We describe the equivariant K-groups of a family of generalized Steinberg varieties that interpolates between the Steinberg variety of a reductive, complex algebraic group and its nilpotent cone in terms of the extended affine Hecke algebra…

We generalize several comparison results between algebraic, semi-topological and topological K-theories to the equivariant case with respect to a finite group.

This article extends the main results of the publication arXiv:2001.01312 to the case of a twisted groupoid. More precisely, it gives a decomposition of the C*-algebra of a twisted locally compact groupoid with Haar system in presence of a…

In this paper, we show the equivalence between two seemingly distinct 2d TQFTs: one comes from the "Coulomb branch index" of the class S theory $T[\Sigma,G]$ on $L(k,1) \times S^1$, the other is the $^LG$ "equivariant Verlinde formula", or…

Let $T$ be a compact torus and $(M,\omega)$ a Hamiltonian $T$-space. We give a new proof of the $K$-theoretic analogue of the Kirwan surjectivity theorem in symplectic geometry by using the equivariant version of the Kirwan map introduced…

Twisted Lie algebroid cohomologies, i.e. with values in representations, are shown to be Lie algebroid homotopy-invariant. Several important classes of examples are discussed. As an application, a generalized version of the Poincar\'e lemma…

Let a compact group G act on real or complex C*-algebras A and B, with A separable and B sigma-unital. We express the G-equivariant Kasparov groups KK_n(A,B) by algebraic K-groups of a certain additive category.

In this paper, a new invariant was built towards the classification of separable C*-algebras of real rank zero, which we call latticed total K-theory. A classification theorem is given in terms of such an invariant for a large class of…

We compare twisted Equivariant K-theory of Sl3Z with untwisted equivariant K-Theory of its universal central extension, St3Z. Using universal coefficient theorems by the authors, the computations explained here give the domain of…

This paper contains two results concerning the equivariant K-theory of toric varieties. The first is a formula for the equivariant K-groups of an arbitrary affine toric variety, generalizing the known formula for smooth ones. In fact, this…

Discussed here is descent theory in the differential context where everything is equipped with a differential operator. To answer a question personally posed by A. Pianzola, we determine all twisted forms of the differential Lie algebras…

For a compact simply connected simple Lie group $G$ with an involution $\alpha$, we compute the $G\rtimes \Z/2$-equivariant K-theory of $G$ where $G$ acts by conjugation and $\Z/2$ acts either by $\alpha$ or by $g\mapsto \alpha(g)^{-1}$. We…

In an earlier paper, the authors introduced partial translation algebras as a generalisation of group C*-algebras. Here we establish an extension of partial translation algebras, which may be viewed as an excision theorem in this context.…

We explain how to define the quantization of q-Hamiltonian SU(2)-spaces as push-forwards in twisted K-homology, and prove a `quantization commutes with reduction' theorem for this setting. As applications, we show how the Verlinde formulas…

We investigate the K-theory of twisted higher-rank-graph algebras by adapting parts of Elliott's computation of the K-theory of the rotation algebras. We show that each 2-cocycle on a higher-rank graph taking values in an abelian group…

Recently it has been shown that D-branes in orientifolds are not always described by equivariant Real K-theory. In this paper we define a previously unstudied twisted version of equivariant Real K-theory which gives the D-brane spectrum for…

The article gives the second part of the treatise on Regular Algebraic $K$-theory (Sections V & VI) of the author. Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected to (but different from)…

Motivated by the Freed-Hopkins-Teleman theorem we study graded equivariant higher twists of $K$-theory for the groups $G = SU(n)$ induced by exponential functors. We compute the rationalisation of these groups for all $n$ and all…

We develop a operator algebraic model for twisted $K$-theory, which includes the most general twistings as a generalized cohomology theory (i.e. all those classified by the unit spectrum $bgl_1(KU)$). Our model is based on strongly…