Let A be a finite dimensional Q-algebra and Γ ⊂ A a Z-order. We classify those A with the property that Z 6 →֒U(Γ). We call this last property the hyperbolic property. We apply this in the case that A = KS a semigroup algebra with K = Q or K = Q( √ −d). In particular, when KS is semi-simple and has no nilpotent elements, we prove that S is an inverse semigroup which is the disjoint union of Higm...

In [4] B. M. Schein considered systems of the form ( ; o; n),where is a set of functions closed under the composition "o" of functions (and hence ( ; o) is a function semigroup) and the set theoretic subtraction "n" (and hence is a subtraction algebra in the sense of [1]). He proved that every subtraction semigroup is isomorphic to a di erence semigroup of invertible functions. B. Zelinka [5] d...

We decompose tensor products of the defining representation of a Cartan type Lie algebra W (n) in the case where the number of tensoring does not exceed the rank of the Lie algebra. As a result, we get a kind of Schur duality between W (n) and a finite dimensional non-semisimple algebra, which is the semi-group ring of the transformation semigroup Tm .

We investigate the minimal number of generators μ and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalities associated with the support hyperplanes of the semigroup. The main result is that for every bound C there exist, up to isomorphism, only finitely divisorial ideals I such that μ(I) ≤ C. It follows that there...

The classical Cuntz semigroup has an important role in the study of C*-algebras, being one of the main invariants used to classify recalcitrant C*-algebras up to isomorphism. We consider C*-algebras that have Hopf algebra structure, and find additional structure in their Cuntz semigroups. We show that in many cases, isomorphisms of Cuntz semigroups that respect this additional structure can be ...

A class of C*-algebras is described for which the homomorphism from C0(0, 1] to the algebra may be classified by means of the Cuntz semigroup functor. Examples are given of algebras—simple and non-simple—for which this classification fails. It is shown that a suitable suspension of the Cuntz semigroup functor deals successfully with some of these counterexamples.

Let B(X) be the algebra of bounded operators on a complex Banach space X. Viewing B(X) as an algebra over R, we study the structure of those irreducible subalgebras which contain nonzero compact operators. In particular, irreducible algebras of trace-class operators with real trace are characterized. This yields an extension of Brauer-type results on matrices to operators in infinite dimensions...

A CP -semigroup (or quantum dynamical semigroup) is a semigroup φ = {φt : t ≥ 0} of normal completely positive linear maps on B(H), H being a separable Hilbert space, which satisfies φt(1) = 1 for all t and is continuous in the natural sense. Let D be the natural domain of the generator L of φ, φt = exp tL. Since the maps φt need not be multiplicative D is typically an operator space, but not a...

A band is a semigroup consisting of idempotents. It is proved that for any field K and any band S with finitely many components, the semigroup algebra K[S] can be embedded in upper triangular matrices over a commutative K-algebra. The proof of a theorem of Malcev [4, Theorem 10] on embeddability of algebras into matrix algebras over a field is corrected and it is proved that if S = F ∪ E is a b...

Given a discrete and countable inverse semigroup $S$ one can study, in analogy to the group case, its geometric aspects. In particular, we equip with natural metric, given by path metric disjoint union of Sch\"{u}tzenberger graphs. This graph, which denote $\Lambda_S$, inherits much structure $S$. this article compare C*-algebra $\mathcal{R}_S$, generated left regular representation on $\ell^2(...