Representations of orbifold groupoids

Orbifold groupoids have been recently widely used to represent both effective and ineffective orbifolds. We show that every orbifold groupoid can be faithfully represented on a continuous family of finite dimensional Hilbert spaces. As a consequence we obtain the result that every orbifold groupoid is Morita equivalent to the translation groupoid of an almost free action of a proper bundle of topological groups.     

A curious nucleus

I describe a simple construction that assigns a pre-nucleus and associated nucleus to each frame. The nature of this nucleus appears to measure the subfitness properties of the parent frame. I pose a few questions concerning this pair.     

A note on unitary representation problem with corrigenda to the articles Weak mixing and unitary representation problem, Bull. Sci. Math. 124 (2000) 517-523 and Identity excluding groups, Bull. Sci. Math. 126 (2002) 763-772

Some of the assertions in the above mentioned articles turn out to be erroneous, as stated, on account of reliance on some earlier works. Here we describe modified (though more restrictive) hypothesis under which the analogues statements hold. We also uphold certain other results by providing a different proof.     

Erratum to “On openness and surjectivity of lifted frame homomorphisms” [Topology Appl. 157 (2010) 2159-2171]

We address and correct an oversight that we have identified in Lemma 3.2 of Dube and Naidoo (2010) [2] and provide counterexamples to the original assertions.     

Irreducible induced representations of ICC-groups

This is an abbreviated version of a part of the author's doctorate thesis accepted by the Fakultät für Mathematik und Informatik der Technischen Universität München on 26 January 1990     

Heisenberg-type groups and intertwining operators

We extend the theorem of Cowling and Haagerup on limits of K-invariant matrix coefficients at approach to the identity, to arbitrary matrix coefficients.     

Some remarks on a paper by Liu and van Rooij

Complementing the work of T.-S. Liu and A.C.M. van Rooij we show that the existence of non-zero translation invariant operators between certain function spaces on a locally compact group implies its amenability.     

On covered prime elements and complete homomorphisms of frames

Abstract

It is a standard fact that the right adjoints h_* of general frame homomor- phisms h : L → M send prime elements to prime elements. Unlike this, the preservation of covered prime elements by complete frame homomorphism is a special fact. Indeed, if L is totally ordered this happens (for arbitrary M) if and only if L is well-ordered. On the other hand, if M is both a frame and a co-frame there is no restriction on L.

This work was motivated by the fact that, in an earlier paper, we erroneously claimed h_* preserves covered primeness for any complete frame homomorphism h.     

Finite traces and representations of the group of infinite matrices over a finite field

The article is devoted to the representation theory of locally compact infinite-dimensional group GLB$\mathbb{GLB}$ of almost upper-triangular infinite matrices over the finite field with q   elements. This group was defined by S.K., A.V., and Andrei Zelevinsky in 1982 as an adequate n=∞$n=\infty$ analogue of general linear groups GL(n,q)$\mathbb{GL}(n,q)$. It serves as an alternative to GL(∞,q)$\mathbb{GL}(\infty ,q)$, whose representation theory is poor.     

Lie groupoids and their natural transformations

We discuss natural transformations in the context of Lie groupoids, and their infinitesimal counterpart. Our main result is an integration procedure that provides smooth natural transformations between Lie groupoid morphisms.     

Moment sets and unitary dual for the diamond group

The diamond group G is a solvable group, semi-direct product of R with a (2n+1)-dimensional Heisenberg group Hn. We consider this group as a first example of a semi-direct product with the form R?N where N is nilpotent, connected and simply connected.Computing the moment sets for G, we prove that they separate the coadjoint orbits and its generic unitary irreducible representations.Then we look for the separation of all irreducible representations. First, moment sets separate representations for a quotient group G⁻ of G by a discrete subgroup, then we can extend G to an overgroup G⁺, extend simultaneously each unitary irreducible representation of G to G⁺ and separate the representations of G by moment sets for G⁺.     

Generalized local cohomology and the canonical element conjecture

We study a generalization of the Canonical Element Conjecture. In particular we show that given a nonregular local ring (A,m) and an i>0, there exist finitely generated A-modules M such that the canonical map from to is nonzero. Moreover, we show that even when M has an infinite projective dimension and i>dim(A), studying these maps sheds light on the Canonical Element Conjecture.     

Free summands of syzygies of modules over local rings

We give a new criterion for a commutative, Noetherian, local ring to be Cohen-Macaulay.     

Pointfree pseudocompactness revisited

We give several internal and external characterizations of pseudocompactness in frames which extend (and transcend) analogous characterizations in topological spaces. In the case of internal characterizations we do not make reference (explicitly or implicitly) to the reals.     

Pricing insurance contracts under Cumulative Prospect Theory

The aim of this paper is to introduce a premium principle which relies on Cumulative Prospect Theory by Kahneman and Tversky. Some special cases of this premium principle have already been studied in the actuarial literature. In the paper, properties of this premium principle are examined.