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A surjective endomorphism or, more generally, a polymorphism in the sense of \cite{SV}, of a compact abelian group $H$ induces a transformation of $L^2(H)$. We study the C*-algebra generated by this operator together with the algebra of…

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the…

Let $G$ be a Lie group, with an invariant non-degenerate symmetric bilinear form on its Lie algebra, let $\pi$ be the fundamental group of an orientable (real) surface $M$ with a finite number of punctures, and let $\bold C$ be a family of…

In this paper, for a locally compact commutative hypergroup $K$ and for a pair $(\Phi_1, \Phi_2)$ of Young functions satisfying sequence condition, we give a necessary condition in terms of aperiodic elements of the center of $K,$ for the…

For a proper, cocompact action by a locally compact group of the form $H \times G$, with $H$ compact, we define an $H \times G$-equivariant index of $H$-transversally elliptic operators, which takes values in $KK_*(C^*H, C^*G)$. This…

The study of harmonic functions on a locally compact group $G$ has recently been transferred to a ``non-commutative'' setting in two different directions: C.-H. Chu and A. T.-M. Lau replaced the algebra $L^\infty(G)$ by the group von…

For a locally compact group $G$, let $A(G)$ denote its Fourier algebra, $M_{cb}(A(G))$ the completely bounded multipliers of $A(G)$, and $A_{M_cb}(G)$ the closure of $A(G)$ in $M_{cb}(A(G))$. We show that, if $A_{M_cb}(G)$ is amenable, then…

We define the notion of strong spectral invariance for a dense Frechet subalgebra A of a Banach algebra B. We show that if A is strongly spectral invariant in a C*-algebra B, and G is a compactly generated polynomial growth Type R Lie…

This paper classifies the derivations of group algebras in terms of the generators and defining relations of the group. If $RG$ is a group ring, where $R$ is commutative and $S$ is a set of generators of $G$ then necessary and sufficient…

By a result of Nagy, the C*-algebra of continuous functions on the q-deformation G_q of a simply connected semisimple compact Lie group G is KK-equivalent to C(G). We show that under this equivalence the K-homology class of the Dirac…

For a locally compact metrizable group $G$, we study the action of $\rm Aut(G)$ on $\rm Sub_G$, the set of closed subgroups of $G$ endowed with the Chabauty topology. Given an automorphism $T$ of $G$, we relate the distality of the…

Let $G$ be a finite group and $H$ a normal subgroup. Starting from $G$-spin models, in which a non-Abelian field ${\mathcal{F}}_H$ w.r.t. $H$ carries an action of the Hopf $C^*$-algebra $D(H;G)$, a subalgebra of the quantum double $D(G)$,…

We extend the geometric side of Arthur's non-invariant trace formula for a reductive group $G$ defined over $\mathbb{Q}$ continuously to a natural space $\mathcal{C}(G(\mathbb{A}^1))$ of test functions which are not necessarily compactly…

Let G be a compact group. Let (X,G) be a standard Borel G-measure space. We show that the group action on (X, G) is transitive if and only if it is ergodic. Using this result, we show that every irreducible covariant representation of a…

A topological space is reversible if each continuous bijection of it onto itself is open. We introduce an analogue of this notion in the category of topological groups: A topological group G is g-reversible if every continuous automorphism…

Let $\Sigma \rightarrow G$ be a twist over a locally compact Hausdorff \'{e}tale groupoid $G$. Given $f$ in the reduced C$^*$-algebra $C_r^*(\Sigma;G)$ with open support $U \subseteq G$ we ask when $f$ lies in the closure of the compactly…

On a Lie group $G$, we investigate the discreteness of the spectrum of Schr\"odinger operators of the form $\mathcal{L} +V$, where $\mathcal{L}$ is a subelliptic sub-Laplacian on $G$ and the potential $V$ is a locally integrable function…

Let $G= \exp(\g)$ be a connected, simply connected nilpotent Lie group. We show that for every $G$-invariant smooth sub-manifold $M$ of $g^*$, there exists an open relatively compact subset $\mathcal{M}$ of $M$ such that for any smooth…

In this article we observe that a locally compact group $G$ is completely determined by the algebraic properties of its Feichtinger's Segal algebra $S_0(G).$ Let $G$ and $H$ be locally compact groups. Then any linear (not necessarily…

For a locally compact, totally disconnected group $G$, a subgroup $H$ and a character $\chi:H \to \mathbb{C}^{\times}$ we define a Hecke algebra $\mathcal{H}_\chi$ and explore the connection between commutativity of $\mathcal{H}_\chi$ and…