# Partial Representations and Partial Group Algebras

@article{Dokuchaev1999PartialRA,
title={Partial Representations and Partial Group Algebras},
author={Mikhailo Dokuchaev and Ruy Exel and Paolo Piccione},
journal={Journal of Algebra},
year={1999},
volume={226},
pages={505-532}
}
• Published 22 March 1999
• Mathematics
• Journal of Algebra
Abstract The partial group algebra of a group G over a field K , denoted by K par ( G ), is the algebra whose representations correspond to the partial representations of G over K -vector spaces. In this paper we study the structure of the partial group algebra K par ( G ), where G is a finite group. In particular, given two finite abelian groups G 1 and G 2 , we prove that if the characteristic of K does not divide the order of G 1 , then K par ( G 1 ) is isomorphic to K par ( G 2 ) if and…
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## References

SHOWING 1-10 OF 34 REFERENCES
Partial Representations and Amenable Fell Bundles over Free Groups
We show that a Fell bundle B = {B_t}_{t \in F}, over an arbitrary free group F, is amenable, whenever it is orthogonal (in the sense that B_x^* B_y = 0, if x and y are distinct generators of F) and
A class ofC*-algebras and topological Markov chains
• Mathematics
• 1980
In this paper we present a class of C*-algebras and point out its close relationship to topological Markov chains, whose theory is part of symbolic dynamics. The C*-algebra construction starts from a
The algebraic structure of group rings
There appeared in 1976 an expository paper by the present author [52] entitled "What is a group ringV This question, rhetorical as it is, may nevertheless be answered directly by saying that for a
Graphs, Groupoids, and Cuntz–Krieger Algebras
• Mathematics
• 1997
We associate to each locally finite directed graphGtwo locally compact groupoidsGandG(★). The unit space ofGis the space of one–sided infinite paths inG, andG(★) is the reduction ofGto the space of
Group Rings and Class Groups
• Mathematics
• 1992
I Some general facts.- II Some notes on representation theory.- III The leading coefficient of units.- IV Class sum correspondence.- V More on the class sum correspondence.- VI Subgroup rigidity.-
CHARACTERISATIONS OF CROSSED PRODUCTS BY PARTIAL ACTIONS
Partial actions of discrete groups on C∗-algebras and the associated crossed products have been studied by Exel and McClanahan. We characterise these crossed products in terms of the spectral
Amenability for Fell bundles.
Given a Fell bundle $\B$, over a discrete group $\Gamma$, we construct its reduced cross sectional algebra $C^*_r(\B)$, in analogy with the reduced crossed products defined for C*-dynamical systems.
SimpleC*-algebra generated by isometries
AbstractWe consider theC*-algebra $$\mathcal{O}_n$$ generated byn≧2 isometriesS1,...,Sn on an infinite-dimensional Hilbert space, with the property thatS1S*1+...+SnS*n=1. It turns out that