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

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

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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• http://mi.mathnet.ru/eng/izv309
• https://doi.org/10.4213/im309
• http://mi.mathnet.ru/eng/izv/v64/i5/p197

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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
2. P. V. Yagodovskii, “$\sigma$-Extensions of discrete multivalued groups”, J. Math. Sci. (N. Y.), 138:3 (2006), 5753–5761
3. V. M. Buchstaber, “$n$-valued groups: theory and applications”, Mosc. Math. J., 6:1 (2006), 57–84
4. P. V. Yagodovsky, “Duality in the theory of finite commutative multivalued groups”, J. Math. Sci. (N. Y.), 174:1 (2011), 97–119
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