Rocky Mountain Journal of Mathematics

Partial representations and their domains

M. Dokuchaev, H.G.G. de Lima, and H. Pinedo

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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

Permanent link to this document
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

Subjects
Primary: 20C25: Projective representations and multipliers
Secondary: 20M30: Representation of semigroups; actions of semigroups on sets 20M50: Connections of semigroups with homological algebra and category theory

Keywords
Partial representations domains of partial factor sets elementary domains

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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References

  • A.H. Clifford and G.B. Preston, The algebraic theory of semigroups, Volume 1, American Mathematical Society, Providence, RI, 1961.
  • M. Dokuchaev, Partial actions: A survey, Cont. Math. 537 (2011), 173–184.
  • M. Dokuchaev and R. Exel, Associativity of crossed products by partial actions, enveloping actions and partial representations, Trans. Amer. Math. Soc. \textbf 357 (2005), 1931–1952.
  • M. Dokuchaev, R. Exel and P. Piccione, Partial representations and partial group algebras, J. Algebra 226 (2000), 505–532.
  • M. Dokuchaev and B. Novikov, Partial projective representations and partial actions, J. Pure Appl. Alg. 214 (2010), 251–268.
  • ––––, Partial projective representations and partial actions II, J. Pure Appl. Alg. 216 (2012), 438–455.
  • M. Dokuchaev, B. Novikov and H. Pinedo, The partial Schur multiplier of a group, J. Algebra 392 (2013), 199–225.
  • M. Dokuchaev and C. Polcino Milies, Isomorphisms of partial group rings, Glasgow Math. J 46 (2004), 161–168.
  • M. Dokuchaev and J.J. Simón, Invariants of partial group algebras of finite $p$-groups, Contemp. Math. 499 (2009), 89–105.
  • ––––, Isomorphisms of partial group rings, Comm. Alg. 44 (2016), 680–696.
  • M. Dokuchaev and N. Zhukavets, On finite degree partial representations of groups, J. Algebra 274 (2004), 309–334.
  • R. Exel, Amenability for Fell bundles, J. reine angew. Math. 492 (1997), 41–73.
  • ––––, Partial action of groups and action of inverse semigroups, Proc. Amer. Math. Soc. 126 (1998), 3481–3494.
  • M. Kellendonk and B. Lawson, Partial actions of groups, Int. J. Algebra. Comp. 14 (2004), 3481–3494.
  • B. Novikov and H. Pinedo, On components of the partial Schur multiplier, Comm. Alg. 42 (2014), 2484–2495.
  • J. Okniński, Semigroup algebras, Dekker, New York, 1991.
  • H. Pinedo, On elementary domains of partial projective representations of groups, Alg. Discr. Math. 15 (2013), 63–82.
  • ––––, The partial Schur multiplier of $S_3$, Int. J. Math. Game Th. Alg. 22 (2014), 405–-417.
  • ––––, Partial projective representations and the partial Schur multiplier: A survey, Boll. Mat. 22 (2015), 167–175.
  • J.C. Quigg and I. Raeburn, Characterizations of crossed products by partial actions, J. Oper. Th. 37 (1997), 311–340.
  • M.B. Szendrei, A note on Birget-Rhodes expansion of groups, J. Pure Appl. Alg. 58 (1989), 93–99.