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On finite degree partial representations of groups. (English) Zbl 1052.20007

In the paper a 1-1 correspondence between the irreducible finite degree partial representations of a group \(G\) and the (usual) irreducible representations of certain ideals of a groupoid algebra constructed from \(G\), is established.

MSC:

20C15 Ordinary representations and characters
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
16S10 Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
16S36 Ordinary and skew polynomial rings and semigroup rings
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References:

[1] Cuntz, J.; Krieger, W., A class of
((C^∗\)-algebras and topological Markov chains, Invent. Math., 56, 251-268 (1980) · Zbl 0434.46045
[2] Dokuchaev, M.; Exel, R.; Piccione, P., Partial representations and partial group algebras, J. Algebra, 226, 1, 505-532 (2000) · Zbl 0954.20004
[3] Exel, R., Partial actions of groups and actions of semigroups, Proc. Am. Math. Soc., 126, 12, 3481-3494 (1998) · Zbl 0910.46041
[4] Exel, R., Amenability for Fell bundles, J. Reine Angew. Math., 492, 41-73 (1997) · Zbl 0881.46046
[5] Exel, R.; Laca, M., Cuntz-Krieger algebras for infinite matrices, J. Reine Angew. Math., 512, 119-172 (1999) · Zbl 0932.47053
[6] Quigg, J. C.; Raeburn, I., Characterizations of crossed products by partial actions, J. Operator Theory, 37, 311-340 (1997) · Zbl 0890.46048
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