Related papers: A noncommutative model for higher twisted K-Theory

An associative algebra with a generalized derivation is called an AsGDer triple. We introduce the operad that encodes AsGDer triples, and prove it is a Koszul operad. Using its Koszul dual cooperad, we introduce the homotopy version of…

In this paper, we prove a general version of Thomsen-Li's Theorem--a Krein-Milman type theorem for C*-algebras. To be precise, for a Markov operator on $C[0,1]$ which preserves certain subspace of $C[0,1]$, we approximate it by an average…

Let $V$ be a freely generated pregraded vertex superalgebra, $H$ a Hamiltonian operator of $V$, and $g$ a diagonalizable automorphism of V commuting with $H$ with modulus $1$ eigenvalues. We prove that the $(g, H)$-twisted Zhu algebra of…

For any topological space there is a sheaf cohomology. A Grothendieck topology is a generalization of the classical topology such that it also possesses a sheaf cohomology. On the other hand any noncommutative $C^*$-algebra is a…

Given a Lie group $G$, a compact subgroup $K$ and a representation $\tau\in\hat K$, we assume that the algebra of $\text{End}(V_\tau)$-valued, bi-$\tau$-equivariant, integrable functions on $G$ is commutative. We present the basic facts of…

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…

In this paper, we present a unified framework for studying cohomology theories of various operators in the context of pseudoalgebras. The central tool in our approach is the notion of a quasi-twilled Lie pseudoalgebra. We introduce two…

The family of Thom spectra $y(n)$ interpolates between the sphere spectrum and the mod two Eilenberg--MacLane spectrum. Computations of Mahowald, Ravenel, Shick, and the authors show that the associative ring spectrum $y(n)$ has type $n$.…

The second author showed how Katsura's construction of the C*-algebra of a topological graph E may be twisted by a Hermitian line bundle L over the edge space E. The correspondence defining the algebra is obtained as the completion of the…

We begin a study of torsion theories for representations of an important class of associative algebras over a field which includes all finite W-algebras of type A, in particular the universal enveloping algebra of gl(n) (or sl(n)) for all…

Quillen introduced a new $K'_0$-theory of nonunital rings and showed that, under some assumptions (weaker than the existence of unity), this new theory agrees with the usual algebraic $K^{alg}_0$-theory. For a field $k$ of characteristic…

We develop a theory of R-module Thom spectra for a commutative symmetric ring spectrum R and we analyze their multiplicative properties. As an interesting source of examples, we show that R-algebra Thom spectra associated to the special…

We introduce a theory of twisted simplicial distributions on simplicial principal bundles, which allow us to capture Bell's non-locality, and the more general notion of quantum contextuality. We leverage the classical theory of simplicial…

This is an expository account of the following result: we can construct a group by means of twisted Z_2-graded vectorial bundles which is isomorphic to K-theory twisted by any degree three integral cohomology class.

We construct by geometric methods a noncommutative model E of the algebra of regular functions on the universal (2-fold) cover M of certain nilpotent coadjoint orbits O for a complex simple Lie algebra g. Here O is the dense orbit in the…

We compute the groupoid homology for the ample groupoids associated with algebraic actions from rings of algebraic integers and integral dynamics. We derive results for the homology of the topological full groups associated with rings of…

A class of non-associative and non-coassociative generalizations of cobraided bialgebras, called cobraided Hom-bialgebras, is introduced. The non-(co)associativity in a cobraided Hom-bialgebra is controlled by a twisting map. Several…

A universal category-theoretical characterization of groupoid equivariant $KK^G$-theory for ${\mathbb{Z}}_2$-graded $C^*$-algebras is established, by observing the ``$KK$-axiom'' that for each $[s,{\cal E} \oplus B, \mathbb{F}] \in…

We present a version of twisted equivariant $K$-theory-$K$-twisted equivariant $K$-theory, and use Grothendieck differentials to compute the $K$ -twisted equivariant $K$-theory of simple simply connected Lie groups. We did the calculation…

We study multivariate generalisations of the classical Wiener--Hopf algebra, which is the C$^*$-algebra generated by the Wiener--Hopf operators, given by the convolutions restricted to convex cones. By the work of Muhly and Renault, this…