Related papers: Bracket map for Heisenberg group and the character…

We investigate the structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group. We work with square integrable representations, and we show that they are those for which we can construct an…

The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…

In this paper we study some geometric properties of surfaces in the Heisenberg group, $\mathcal{H}_{3}.$ We obtain, using the Gauss map for Lie groups, a partial classification of minimal graphs in $\mathcal{H}_{3}.$ We also proof the non…

Is every locally compact abelian group which admits a Heisenberg central extension isomorphic to the product of a locally compact abelian group and its Pontryagin dual? An affirmative answer is obtained for all the commonly occurring types…

The study of actions of countable groups by automorphisms of compact abelian groups has recently undergone intensive development, revealing deep connections with operator algebras and other areas. The discrete Heisenberg group is the…

In this paper we study certain groups of bilipschitz maps of the boundary minus a point of a negatively curved space that is an abelian-by-cyclic solvable Lie group, where the extension is given by a matrix whose eigenvalues all lie outside…

In this paper, we introduce the notions of matching matrices in groups and vector spaces, which lead to some necessary conditions for existence of acyclic matching in abelian groups and its linear analogue. We also study the linear local…

In the context of a connected, simply connected, nilpotent Lie group, whose representations are square-integrable modulo the center, we find characterization results of extra-invariant spaces under the left translations associated with the…

We use assembly maps to study $\mathbf{TC}(\mathbb{A}[G];p)$, the topological cyclic homology at a prime $p$ of the group algebra of a discrete group $G$ with coefficients in a connective ring spectrum $\mathbb{A}$. For any finite group, we…

A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite…

The class of locally compact near abelian groups is introduced and investigated as a class of metabelian groups formalizing and applying the concept of scalar multiplication. The structure of locally compact near abelian groups and its…

In his 1951 book "Infinite Abelian Groups", Kaplansky gives a combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group. In this paper we first use partial maps on…

The dual Lie bialgebra of a certain ``quasitriangular'' Lie bialgebra structure on the Heisenberg Lie algebra determines a (non-compact) Poisson--Lie group G. The compatible Poisson bracket on G is non-linear, but it can still be realized…

This paper considers non-Abelian homology groups of a group diagram introduced as homotopy groups of a simplicial change. We prove a theorem stating that the non-Abelian homology groups of a group diagram are isomorphic to the homotopy…

Motivated by the Lawrence-Krammer-Bigelow representations of the classical braid groups, we study the homology of unordered configurations in an orientable genus-$g$ surface with one boundary component, over non-commutative local systems…

A parametrization of irreducible unitary representations associated with the regular adjoint orbits of a hyperspecial compact subgroup of a reductive group over a non-dyadic non-archimedean local filed is presented. The parametrization is…

Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated…

Let F be a local field. In the case of F being the real field, Pierre Cartier constructed Heisenberg-Weil representations of a Heisenberg group in families using non-self-dual lattices. This result was later reformulated by Jae-Hyun Yang in…

We determine the groups of automorphisms and their orbits for nilpotent Lie algebras of class 2 and small dimension, over arbitrary fields (including the characteristic 2 case).

We provide detailed calculations for the classification of representations of compact simple Lie groups with non-empty boundary in the orbit space, first announced in a previous paper [arXiv:2112.00513] by the same authors.