Related papers: Euclidean Algebras

We introduce a notion of a uniform structure on the set of all representations of a given separable, not necessarilly commutative $C^*$-algebra $\mathfrak{A}$ by introducing a suitable family of metrics on the set of representations of…

Let $K$ be a compact metric space and let $\gamma = (\gamma_1, \dots, \gamma_n)$ be a system of proper contractions on $K$. We study a C*-algebra $\mathcal{MC}_{\gamma_1, \dots, \gamma_n}$ generated by all multiplication operators by…

We propose a definition of a "$C^*$-Eberlein" algebra, which is a weak form of a $C^*$-bialgebra with a sort of "unitary generator". Our definition is motivated to ensure that commutative examples arise exactly from semigroups of…

Let Z be the zero set of a holomorphic map from C^n to C^k. Assume that Z is non-empty. We prove that for any r > 0, the Gaussian measure of the Euclidean r-neighborhood of Z is at least as large as the Gaussian measure of the Euclidean…

Henkin functionals on non-commutative $\mathrm{C}^*$-algebras have recently emerged as a pivotal link between operator theory and complex function theory in several variables. Our aim in this paper is characterize these functionals through…

I review certain results in harmonic analysis for systems whose configuration space is a compact Lie group. The results described involve a heat kernel measure, which plays the same role as a Gaussian measure on Euclidean space. The main…

The algebra dual to Woronowicz's deformation of the 2-\-di\-men\-sion\-al Euclidean group is constructed. The same algebra is obtained from $SU_{q}(2)$ via contraction on both the group and algebra levels.

Let $\mathfrak{g}$ be a finite-dimensional complex Lie algebra and $\textrm{HLie}_{m}(\mathfrak{g})$ be the affine variety of all multiplicative Hom-Lie algebras on $\mathfrak{g}$. We use a method of computational ideal theory to describe…

A null vector is an algebraic quantity with square equal to zero. I denote the universal algebra generated by taking all sums and products of null vectors over the real or complex numbers by N. The rules of addition and multiplication in N…

Inside the double affine Hecke algebra of type $GL_n$, which depends on two parameters $q$ and $\tau$, we define a subalgebra $\mathbb{H}^{\mathfrak{gl}_n}$ that may be thought of as a $q$-analogue of the degree zero part of the…

In a recent paper, Pardo and the first named author introduced a class of C*-algebras which which are constructed from an action of a group on a graph. This class was shown to include many C*-algebras of interest, including all Kirchberg…

Lie algebraic techniques are powerful and widely-used tools for studying dynamics and metrology in quantum optics. When the Hamiltonian generates a Lie algebra with finite dimension, the unitary evolution can be expressed as a finite…

Quantitative algebras are $\Sigma$-algebras acting on metric spaces, where operations are nonexpanding. Mardare, Panangaden and Plotkin introduced 1-basic varieties as categories of quantitative algebras presented by quantitative equations.…

Let $A$ be a unital associative algebra over a field $k$. All unital associative algebras containing $A$ as a subalgebra of a given codimension $\mathfrak{c}$ are described and classified. For a fixed vector space $V$ of dimension…

This is an expository book on unitary representations of topological groups, and of several dual spaces, which are spaces of such representations up to some equivalence. The most important notions are defined for topological groups, but a…

Let G be a discrete group and $\Gamma$ an almost normal subgroup. The operation of cosets concatanation extended by linearity gives rise to an operator system that is embeddable in a natural C* algebra. The Hecke algebra naturally embeds as…

Here we examine some connections between the notions of generalized arithmetic means, geodesics, Lagrange-Hamilton dynamics and Bregman divergences. In a previous paper we developed a predictive interpretation of generalized arithmetic…

We use an embedding of the symmetric $d$th power of any algebraic curve $C$ of genus $g$ into a Grassmannian space to give algorithms for working with divisors on $C$, using only linear algebra in vector spaces of dimension $O(g)$, and…

Starting from gravity as a Chern-Simons action for the AdS algebra in five dimensions, it is possible to deform the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein-Hilbert action plus…

We show that in two dimensions the incompressible Euler equations can be re-expressed in terms of an abelian gauge theory with a Chern-Simons term. The magnetic field corresponds to fluid vorticity and the electric field is the product of…