The Grothendieck-Serre formula for the difference between the Hilbert function and Hilbert polynomial of a graded algebra is generalized for bigraded standard algebras. This is used to get a similar formula for the difference between the Bhattacharya function and Bhattacharya polynomial of two m-primary ideals I and J in a local ring (A, m) in terms of local cohomology modules of Rees algebras ...

In this paper we introduce controlled *-g-frame and *-g-multipliers in Hilbert C*-modules and investigate the properties. We demonstrate that any controlled *-g-frame is equivalent to a *-g-frame and define multipliers for (C,C')- controlled*-g-frames .

let $ m , n in mathbb{n}$, $d$ be a division ring, and $m_{m times n}(d)$ denote the bimodule of all $m times n$ matrices with entries from $d$. first, we characterize one-sided submodules of $m_{m times n}(d)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $d$. next, we introduce the notion of a nest module of matrices with entries from $d$. we ...

Abstract. We consider a class of C-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner’s Toeplitz algebras. By exhibiting a homotopy of quasihomomorphisms, we prove that those algebras are K-contractible. One special case is closely related to the Rieffel-Wiener-Hopf extension of a crossed product b...

The Hilbert scheme of point modules was introduced by Artin-Tate-Van den Bergh to study non-commutative graded algebras. The key tool is the construction of a map from the algebra to a twisted ring on this Hilbert scheme. In this paper, we study moduli stacks of more general “fat” point modules, and show that there is a similar map to a twisted ring associated to the stack. This is used to prov...

In this article we survey some of the recent goings-on in the classification programme of C-algebras, following the interesting link found between the Cuntz semigroup and the classical Elliott invariant and the fact that the Elliott conjecture does not hold at its boldest. We review the construction of this object both by means of positive elements and via its recent interpretation using counta...

Abstract We calculate the extension groups between simple modules of pro- p -Iwahori Hecke algebras.

We give a solution, via operator spaces, of an old problem in the Morita equivalence of C*-algebras. Namely, we show that C*-algebras are strongly Morita equivalent in the sense of Rieffel if and only if their categories of left operator modules are isomorphic via completely contractive functors. Moreover, any such functor is completely isometrically isomorphic to the Haagerup tensor product (=...

In this paper we consider algebras with involution over a ring C which is given by the quadratic extension by i of an ordered ring R. We discuss the -representation theory of such -algebras on pre-Hilbert spaces over C and develop the notions of Rieffel induction and formal Morita equivalence for this category analogously to the situation for C-algebras. Throughout this paper the notion of posi...