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Sibirsk. Mat. Zh., 2009, Volume 50, Number 6, Pages 1401–1412 (Mi smj2059)  

This article is cited in 1 scientific paper (total in 1 paper)

On superalgebras over operads

S. N. Tronin

Kazan State University, Faculty of Mechanics and Mathematics, Kazan

Abstract: We show that the class of varieties of multioperator superalgebras, defined by multilinear identities and considered up to rational equivalence, coincides with the class of varieties of superalgebras over an operad. We define the concepts of Grassmann and Clifford envelopes in the most general case and study their properties. We define the concept of module over a superalgebra over an operad and the concept of universal enveloping superalgebra for an algebra over an operad and study their properties.

Keywords: superalgebra, operad, identity.

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English version:
Siberian Mathematical Journal, 2009, 50:6, 1106–1114

Bibliographic databases:

UDC: 512
Received: 23.01.2008

Citation: S. N. Tronin, “On superalgebras over operads”, Sibirsk. Mat. Zh., 50:6 (2009), 1401–1412; Siberian Math. J., 50:6 (2009), 1106–1114

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. A. N. Abyzov, Yu. A. Alpin, N. A. Koreshkov, M. F. Nasrutdinov, S. N. Tronin, “Algebraicheskie issledovaniya v Kazanskom universitete ot V. V. Morozova do nashikh dnei”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2012, 44–59  mathnet
  • Сибирский математический журнал Siberian Mathematical Journal
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