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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.

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Correspondence to S. N. Tronin.

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Original Russian Text Copyright © 2009 Tronin S. N.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 6, pp. 1401–1412, November–December, 2009.

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Tronin, S.N. On superalgebras over operads. Sib Math J 50, 1106–1114 (2009). https://doi.org/10.1007/s11202-009-0122-4

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  • DOI: https://doi.org/10.1007/s11202-009-0122-4

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