Related papers: Heisenberg Groups via Algebra
We introduce a cohomology set for groups defined by algebraic difference equations and show that it classifies torsors under the group action. This allows us to compute all torsors for large classes of groups. We also develop some tools for…
We study some of the possibilities for formulating the Heisenberg relation of quantum mechanics in mathematical terms. In particular, we examine the framework discussed by Murray and von Neumann, the family (algebra) of operators affiliated…
Given a graded ample Hausdorff groupoid, we realise its graded Steinberg algebra as a partial skew inverse semigroup ring. We use this to show that for a partial action of a discrete group on a locally compact Hausdorff topological space,…
In this work, we use probability groups, introduced by Harrison in 1979, as a tool to study a semisimple Hopf algebra $H$ with a commutative character ring and prove that the algebra generalized by the dual probability group is the center…
Hom-algebras over a PROP are defined and studied. Several twisting constructions for Hom-algebras over a large class of PROPs are proved, generalizing many such results in the literature. Partial classification of Hom-algebras over a PROP…
We study some extension of a discrete Heisenberg group coming from the theory of loop-groups and find invariants of conjugacy classes in this group. In some cases including the case of the integer Heisenberg group we make these invariants…
The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…
We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…
In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.
In this expositional paper, we discuss commutative algebra -- a study inspired by the properties of integers, rational numbers, and real numbers. In particular, we investigate rings and ideals, and their various properties. After, we…
In the present paper we study some homotopy invariants which can be defined by means of bundles with fiber a matrix algebra. We also introduce some generalization of the Brauer group in the topological context and show that any its element…
We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices. Each finite directed acyclic graph admits countably many structures of a generalized…
Schwinger's algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids.…
It is well known that certain features of a quantum theory cannot be described in the standard picture on a Hilbert space. In particular, this happens when we try to formally frame a quantum field theory, or a thermodynamic system with…
Using the general theory of [10] ( hep-th 9412058 ), quantum Poincar\'e groups (without dilatations) are described and investigated. The description contains a set of numerical parameters which satisfy certain polynomial equations. For most…
A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.
By means of techniques from the Morita equivalence theory, we get finitely generated and projective modules over the quantum Heisenberg manifolds. This enables us to get some information about the range of the trace of these algebras, at…
We begin the study of unitary representations of Hecke algebras of complex reflections groups. We obtain a complete classification for the Hecke algebra of the symmetric group $\mathfrak{S}_n$ over the complex numbers. Interestingly, the…
In this work we study the induction theory for Hopf group coalgebra. To reach this goal we define a substructure B of a Hopf group coalgebra $H$, called subHopf group coalgebra. Also, we introduced the definition of Hopf group suboalgebra…
The purpose of this note is to make some connection between the sub-Riemannian geometry on Carnot-Caratheodory groups and symplectic geometry. We shall concentrate here on the Heisenberg group, although it is transparent that almost…