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}
}
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
Units in integral group rings
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
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
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
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…
On the C*-algebra of a one-parameter semigroup of isometries: In memory of David M. topping
...
1
2
3
4
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