A C *-algebra A is called an ideal C * -algebra (or equally a dual algebra) if it is an ideal in its bidual A**. M.C.F. Berglund proved that subalgebras and quotients of ideal C*-algebras are also ideal C*-algebras, that a commutative C *-algebra A is an ideal C *-algebra if and only if it is isomorphicto C (Q) for some discrete space ?. We investigate ideal J*-algebras and show that the a...

Let G be a finite-dimensional Poisson algebraic, Lie or formal group. We show that the center of the quantization of G provided by an Etingof–Kazhdan functor is isomorphic as an algebra to the Poisson center of the algebra of functions on G. This recovers and generalizes Duflo’s theorem which gives an isomorphism between the center of the enveloping algebra of a finite-dimensional Lie algebra a...

Ladkin and Maddux [LaMa87] showed how to interpret the calculus of time intervals defined by Allen [AZ2831 in terms of representations of a particular relation algebra, and proved that this algebra has a unique countable representation up to isomorphism. In this paper, we . consider the algebra An of n-intervals, which coincides with Allen’s algebra for n=2, and prove that An has a unique count...

The groups whose orders factorise into at most four primes have been described (up to isomorphism) in various papers. Given such an order n, this paper exhibits a new explicit and compact determination of the isomorphism types n together with effective algorithms enumerate, construct, identify these groups. are implemented for computer algebra system GAP.

Algorithms to decide isomorphism of modules have been honed continually over the last 30 years, and their range of applicability has been extended to include modules over a wide range of rings. Highly efficient computer implementations of these algorithms form the bedrock of systems such as GAP and Magma, at least in regard to computations with groups and algebras. By contrast, the fundamental ...

We answer a question of E. Kirchberg (personal communication): does the relative commutant of a separable C*-algebra in its ultrapower depend on the choice of the ultrafilter? All algebras and all subalgebras in this note are C*-algebras and C*subalgebras, respectively, and all ultrafilters are nonprincipal ultrafilters on N. Our C*-terminology is standard (see e.g., [2]). In the following U ra...

Let G be a connected semisimple algebraic group over an algebraically closed field of characteristic zero. A canonical presentation by generators and relations of the algebra of regular functions on G is found. The conjectures of D.Flath and J.Towber, [FT], are proved. (1) Let G be a connected semisimple algebraic group over an algebraically closed field k of characteristic zero. We obtain here...

Classical Segal–Bargmann theory studies three Hilbert space unitary isomorphisms that describe the wave-particle duality and configuration space-phase space. In this work, we generalized these concepts to Clifford algebra-valued functions. We establish among of square-integrable functions on $$\mathbb {R}^n$$ with respect a Gaussian measure, monogenic {R}^{n+1}$$ another measure linear function...

The paper continues the study of differential Banach *algebras AS and FS of operators associated with symmetric operators S on Hilbert spaces H. The algebra AS is the domain of the largest *-derivation δS of B(H) implemented by S and the algebra FS is the closure of the set of all finite rank operators in AS with respect to the norm ‖A‖ = ‖A‖+‖δS(A)‖. When S is selfadjoint, FS is the domain of ...

A full rational CFT, consistent on all orientable world sheets, can be constructed from the underlying chiral CFT, i.e. a vertex algebra, its representation category C, and the system of chiral blocks, once we select a symmetric special Frobenius algebra A in the category C [I]. Here we show that the construction of [I] can be extended to unoriented world sheets by specifying one additional dat...