This article is cited 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.

UDC: 512

Received: 23.01.2008

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

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