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 ...

Abstact We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by n generators and n(n−1) 2 relations for n 6 7. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra. Precise descriptions of graphs (maps) ...

In this note I discuss some aspects of a formulation of quantum mechanics based entirely on the Jordan algebra of observables. After reviewing some facts of the formulation in the C∗-approach I present a Jordan-algebraic Hilbert space construction (inspired by the usual GNS-construction), thereby obtaining a real Hilbert space and a (Jordan-) representation of the algebra of observables on this...

We initiate a study of Hilbert modules over the polynomial algebra A = C[z1, . . . , zd] that are obtained by completing A with respect to an inner product having certain natural properties. A standard Hilbert module is a finite multiplicity version of one of these. Standard Hilbert modules occupy a position analogous to that of free modules of finite rank in commutative algebra, and their quot...

The formalism of local coordinates on infinite-dimensional Hilbert manifolds is introduced. Images of charts on the manifolds are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. The corresponding local coordinate form of algebra of tensor fields on Hilbert manifolds is constructed. A single tensor equation in the formalism is shown to produc...

The paper contains constructions of Hilbert systems for the action of the circle group T using subgroups of implementable Bogoljubov unitaries w.r.t. Fock representations of the Fermion algebra for suitable data of the selfdual framework: H is the reference Hilbert space, Γ the conjugation and P a basis projection on H. According to a general result for Hilbert systems of this type, the group C...

We introduce the notion of automorphic symbol generalizing the classical modular symbol and use it to attach very general p-adic L-functions to nearly ordinary Hilbert automorphic forms. Then we establish an exact control theorem for the p-adically completed cohomology of a Hilbert modular variety localized at a suitable nearly ordinary maximal ideal of the Hecke algebra. We also show its freen...