## Rocky Mountain Journal of Mathematics

### Partial representations and their domains

#### Abstract

We study the structure of the partially or\-dered set of the elementary domains of partial (linear or projective) representations of groups. This provides an important information on the lattice of all domains. Some of these results are obtained through structural facts on the ideals of the semigroup $\mathcal{S} _3(G)$, a quotient of Exel's semigroup $\mathcal{S} (G)$, which plays a crucial role in the theory of partial projective representations. We also fill a gap in the proof of an earlier result on the structure of partial group representations.

#### Article information

Source
Rocky Mountain J. Math., Volume 47, Number 8 (2017), 2565-2604.

Dates
First available in Project Euclid: 3 February 2018

https://projecteuclid.org/euclid.rmjm/1517648600

Digital Object Identifier
doi:10.1216/RMJ-2017-47-8-2565

Mathematical Reviews number (MathSciNet)
MR3760307

Zentralblatt MATH identifier
06840989

#### Citation

Dokuchaev, M.; Lima, H.G.G. de; Pinedo, H. Partial representations and their domains. Rocky Mountain J. Math. 47 (2017), no. 8, 2565--2604. doi:10.1216/RMJ-2017-47-8-2565. https://projecteuclid.org/euclid.rmjm/1517648600

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