Given a classical symmetric pair, (G, K), with g = Lie(G), we provide descriptions of the Hilbert series of the algebra of K-invariant vectors in the associated graded algebra of U(g) viewed as a K-representation under restriction of the adjoint representation. The description illuminates a certain stable behavior of the Hilbert series, which is investigated in a case-by-case basis. We note tha...

Let $R$ be a positively graded algebra over field. We say that is Hilbert-cyclotomic if the numerator of its reduced Hilbert series has all roots on unit circle. Such rings arise naturally in commutative algebra, numerical semigroup theory and Ehrhart theory. If standard graded, we prove that, under additional hypothesis Koszul or an irreducible $h$-polynomial, algebras coincide with complete i...

The aim of this paper is to introduce the notion of fantastic deductive systems on generalizations of fuzzy structures, and to emphasize their role in the probability theory on these algebras. We give a characterization of commutative pseudo-BE algebras and we generalize an axiom system consisting of four identities to the case of commutative pseudo-BE algebras. We define the fantastic deductiv...

Hilbert C∗-modules are useful tools in AW ∗-algebra theory, theory of operator algbras, operator K-theory, group representation theory and theory of operator spaces. The theory of Hilbert C∗-modules is very interesting on its own. In this paper we give fundamentals of the theory of Hilbert C∗-modules and examine some ways in which Hilbert C∗-modules differ from Hilbert spaces.

Let (A,Ao) be a topological quasi *-algebra, which means in particular that Ao is a topological *-algebra, dense in A. Let πo be a *-representation of Ao in some pre-Hilbert space D ⊂ H. Then we present several ways of extending πo, by closure, to some larger quasi *-algebra contained in A, either by Hilbert space operators, or by sesquilinear forms on D. Explicit examples are discussed, both a...

Let H be a full Hilbert bimodule over a C-algebra A. We show that the Cuntz–Pimsner algebra associated to H is exact if and only if A is exact. Using this result, we give alternative proofs for exactness of reduced amalgemated free products of exact C– algebras. In the case that A is a finite–dimensional C–algebra, we also show that the Brown–Voiculescu topological entropy of Bogljubov automorp...

Nagata gave a fundamental sufficient condition on group actions on finitely generated commutative algebras for finite generation of the subalgebra of invariants. In this paper we consider groups acting on noncommutative algebras over a field of characteristic zero. We characterize all the T-ideals of the free associative algebra such that the algebra of invariants in the corresponding relativel...

We analzye Rieffel’s construction of generalized fixed point algebras in the setting of group actions on Hilbert modules. Let G be a locally compact group acting on a C∗-algebra B. We construct a Hilbert module F over the reduced crossed product of G and B, using a pair (E, R), where E is an equivariant Hilbert module over B and R is a dense subspace of E with certain properties. The generalize...

In [13], Woronowicz introduced a functional calculus for normal regular operators in a Hilbert C-module. In this paper, we have translated several concepts known in Hilbert space theory to the Hilbert C-module framework. We looked for instance into the functional calculus for strictly positive elements, the Fuglede Putnam theorem in Hilbert C-modules, commuting normal regular operators, ... It ...

The notion of structural completeness has received considerable attention for many years. A translation to algebra gives: a quasivariety is structurally complete if it is generated by its free algebras. It appears that many deductive systems (quasivarieties), like S5 or MVn fails structural completeness for a rather immaterial reason. Therefore the adjusted notion was introduced: almost structu...