Related papers: Arens-Michael enveloping algebras and analytic sma…

It is shown that if A is a separable, exact C*-algebra which satisfies the Universal Coefficient Theorem (UCT) and has a faithful, amenable trace, then A admits a trace-preserving embedding into a simple, unital AF-algebra with unique…

Given a locally finite graded set A and a commutative, associative operation on A that adds degrees, we construct a commutative multiplication * on the set of noncommutative polynomials in A which we call a quasi-shuffle product; it can be…

Let $G$ denote an infinite-dimensional Heisenberg-like group, which is a class of infinite-dimensional step 2 stratified Lie groups. We consider holomorphic functions on $G$ that are square integrable with respect to a heat kernel measure…

Let G be a Lie group and E be a locally convex topological G-module. If E is sequentially complete, then E and its space of smooth vectors are modules for the algebra D(G) of compactly supported smooth functions on G. However, the module…

Given a Banach algebra $ \mathcal{A} $ and a continuous homomorphism $\sigma$ on it, the notion of $\sigma$-biflatness for $ \mathcal{A} $ is introduced. This is a generalization of biflatness and it is shown that they are distinct. The…

We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…

We define cup coproducts for Hopf cyclic cohomology of Hopf algebras and for its dual theory. We show that for universal enveloping algebras and group algebras our coproduct recovers the standard coproducts on Lie algebra homology and group…

Let $G$ be an abelien group, $\epsilon$ an anti-bicharacter of $G$ and $L$ a $G$-graded $\epsilon$ Lie algebra (color Lie algebra) over $\K$ a field of characteristic zero. We prove that all $G$-graded, positive filtered $A$ such that the…

$HC_*(A \rtimes G)$ is the cyclic homology of the crossed product algebra $A \rtimes G.$ For any $g \epsilon G$ we will define a homomorphism from $HC_*^g(A),$ the twisted cylic homology of $A$ with respect to $g,$ to $HC_*(A \rtimes G).$…

Let $\mathfrak{g}$ be a Borcherds-Bozec algebra, $U(\mathfrak{g})$ be its universal enveloping algebra and $U_{q}(\mathfrak{g})$ be the corresponding quantum Borcherds-Bozec algebra. We show that the classical limit of $U_{q}(\mathfrak{g})$…

It is shown that if A is an AF algebra then a crossed product of A by the integers can be embedded into an AF algebra if and only if the crossed product is stably finite. This equivalence follows from a simple K-theoretic characterization…

We show that for algebraic groups over local fields of characteristic zero, the following are equivalent: Every homomorphism has a closed image, every unitary representation decomposes into a direct sum of finite-dimensional and mixing…

We study Lie algebras endowed with an abelian complex structure which admit a symplectic form compatible with the complex structure. We prove that each of those Lie algebras is completely determined by a pair (U,H) where U is a complex…

Let ${\mathcal G}$ be a locally compact group. In continuation of our studies on the first and second duals of measure algebras by the use of the theory of generalised functions, here we study the C$^*$-subalgebra $GL_0({\mathcal G})$ of…

Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space L(H) of linear bounded operators on H with weak operator topology. We prove that if U is a measurable map from G to L(H) then it…

We give some general results on the ring structure of Hochschild cohomology of smash products of algebras with Hopf algebras. We compute this ring structure explicitly for a large class of finite dimensional Hopf algebras of rank one.

Let $G$ be the adjoint group of a real simple Lie algebra $\mathfrak{g}_0$ equal either $\mathfrak{s}\mathfrak{u}(n,1)$ or $\mathfrak{s}\mathfrak{o}(n,1),$ $K$ its maximal compact subgroup, ${\cal U}(\mathfrak{g})$ the universal enveloping…

We review the construction of the multiparametric quantum group $ISO_{q,r}(N)$ as a projection from $SO_{q,r}(N+2) $ and show that it is a bicovariant bimodule over $SO_{q,r}(N)$. The universal enveloping algebra $U_{q,r}(iso(N))$,…

We investigate Hopf algebroids in the category of $L$-complete modules over a commutative Noetherian regular complete local ring. The main examples are provided by the Hopf algebroids associated to Lubin-Tate spectra in the K(n)-local…

In this paper we study the homogenized algebra $B$ of the enveloping algebra $U$ of the Lie algebra sl(2,C). We look first to connections between the category of graded left $B$- modules and the category of $U$-modules, then we prove $B$ is…