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Izv. RAN. Ser. Mat., 2000, Volume 64, Issue 5, Pages 197–224 (Mi izv309)  

This article is cited in 4 scientific papers (total in 4 papers)

Linear deformations of discrete groups and constructions of multivalued groups

P. V. Yagodovskii


Abstract: We construct deformations of discrete multivalued groups described as special deformations of their group algebras in the class of finite-dimensional associative algebras. We show that the deformations of ordinary groups producing multivalued groups are defined by cocycles with coefficients in the group algebra of the original group and obtain classification theorems on these deformations. We indicate a connection between the linear deformations of discrete groups introduced in this paper and the well-known constructions of multivalued groups. We describe the manifold of three-dimensional associative commutative algebras with identity element, fixed basis, and a constant number of values. The group algebras of $n$-valued groups of order three (three-dimensional $n$-group algebras) form a discrete set in this manifold.

DOI: https://doi.org/10.4213/im309

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English version:
Izvestiya: Mathematics, 2000, 64:5, 1065–1089

Bibliographic databases:

MSC: 16S80, 20N15, 16S34, 05E30, 20N20, 05B30, 05C25, 20B25
Received: 25.03.1998

Citation: P. V. Yagodovskii, “Linear deformations of discrete groups and constructions of multivalued groups”, Izv. RAN. Ser. Mat., 64:5 (2000), 197–224; Izv. Math., 64:5 (2000), 1065–1089

Citation in format AMSBIB
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  • https://doi.org/10.4213/im309
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. P. V. Yagodovskii, “Representations of multivalued groups on graphs”, Russian Math. Surveys, 57:1 (2002), 173–174  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. P. V. Yagodovskii, “$\sigma$-Extensions of discrete multivalued groups”, J. Math. Sci. (N. Y.), 138:3 (2006), 5753–5761  mathnet  crossref  mathscinet  zmath  elib  elib
    3. V. M. Buchstaber, “$n$-valued groups: theory and applications”, Mosc. Math. J., 6:1 (2006), 57–84  mathnet  mathscinet  zmath
    4. P. V. Yagodovsky, “Duality in the theory of finite commutative multivalued groups”, J. Math. Sci. (N. Y.), 174:1 (2011), 97–119  mathnet  crossref
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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