Related papers: Equivariant K-theory of compact Lie groups with in…

A group equivariant $KK$-theory for rings will be defined and studied in analogy to Kasparov's $KK$-theory for $C^*$-algebras. It is a kind of linearization of the category of rings by allowing addition of homomorphisms, imposing also…

We show that the isotropy action of a homogeneous space $G/K$, where $G$ and $K$ are compact, connected Lie groups and $K$ is defined by an automorphism on $G$, is equivariantly formal and that $(G, K)$ is a Cartan pair.

In this paper we give a geometric construction of the Borel equivariant (co)homology for spaces with a $G$-action, where $G$ is a compact Lie group with the property that the adjoint representation is orientable. A nice feature of these…

This paper explores further the computation of the twisted K-theory and K-homology of compact simple Lie groups, previously studied by Hopkins, Moore, Maldacena-Moore-Seiberg, Braun, and Douglas, with a focus on groups of rank 2. We give a…

Let $\mathcal{G}$ be an algebraic quantum group. We introduce an equivariant algebraic $kk$-theory for $\mathcal{G}$-module algebras. We study an adjointness theorem related with smash product and trivial action. We also discuss a duality…

We prove the deformation invariance of the quantum homogeneous spaces of the q-deformation of simply connected simple compact Lie groups over the Poisson-Lie quantum subgroups, in the equivariant KK-theory with respect to the translation…

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…

Equivariant T-duality triples of locally compact abelian groups are considered. The motivating example dealing with the group $\R^n$ containing a lattice $\Z^n$ comes with an isomorphism in twisted equivariant K-theory.

Let G=SU(2) and let \Omega G denote the space of continuous based loops in G, equipped with the pointwise conjugation action of G. It is a classical fact in topology that the ordinary cohomology H^*(\Omega G) is a divided polynomial algebra…

In this note we classify all homogeneous spaces $G/H$ admitting a $G$-invariant $G_2$-structure, assuming that $G$ is a compact Lie group and $G$ acts effectively on $G/H$. They include a subclass of all homogeneous spaces $G/H$ with a…

In this paper, for a compact Lie group action,we prove the anomaly formula and the functoriality of the equivariant Bismut-Cheeger eta forms with perturbation operators when the equivariant family index vanishes. In order to prove them, we…

For G a complex reductive group and X a smooth projective or convex quasi-projective polarized G-variety we construct a formal map in quantum K-theory from the equivariant quantum K-theory $QK^G(X)$ to the quantum K-theory of the git…

We compare the K-theories of symplectic quotients with respect to a compact connected Lie group and with respect to its maximal torus, and in particular we give a method for computing the former in terms of the latter. More specifically,…

We compute the equivariant K-homology of the groups PSL_2 of imaginary quadratic integers with trivial and non-trivial class-group. This was done before only for cases of trivial class number. We rely on reduction theory in the form of the…

Let $k$ be a field of characteristic zero, let $G$ be a connected reductive algebraic group over $k$ and let $\mathfrak{g}$ be its Lie algebra. Let $k(G)$, respectively, $k(\mathfrak{g})$, be the field of $k$-rational functions on $G$,…

We present a new probabilistic model of compact commutative Lie groups that produces invariant-equivariant and disentangled representations of data. To define the notion of disentangling, we borrow a fundamental principle from physics that…

In this paper we analyse for a $G$-$C^{*}$-algebra $A$ to which extent one can calculate the $K$-theory of the reduced crossed product $K(A\rtimes_{r}G)$ from the $K$-theory spectrum $K(A)$ with the induced $G$-action. We also consider some…

Given a Lie group $G$ with finitely many components and a compact Lie group A which acts on $G$ by automorphisms, we prove that there always exists an A-invariant maximal compact subgroup K of G, and that for every such K, the natural map…

We define a certain class of simple varieties over a field $k$ by a constructive recipe and show how to control their (equivariant) truncating invariants. Consequently, we prove that on simple varieties: (i) if $k=\overline{k}$ and…

Let $G$ be a compact Lie group, $H$ a closed subgroup of maximal rank and $X$ a topological $G$-space. We obtain a variety of results concerning the structure of the $H$-equivariant K-ring $K_H^*(X)$ viewed as a module over the…