Alternating and symmetric superpowers of metric generalized Jordan superpairs.

Abstract

This article introduces and studies the alternating and symmetric superpowers of metric generalized Jordan superpairs. These constructions are obtained by transferring the corresponding superpower operations through the Faulkner construction, which relates these structures to certain modules over Lie superalgebras. The authors also revisit the tensor product construction in this context and analyze its algebraic properties. The work is developed over base fields of characteristic different from 2 and shows how these constructions extend the theory of generalized Jordan superpairs.