Alternating and symmetric superpowers of metric generalized Jordan superpairs

TL;DR

This paper introduces and analyzes the concepts of alternating and symmetric superpowers of metric generalized Jordan superpairs, extending tensor product constructions through the Faulkner framework, with considerations for field characteristics.

Contribution

It defines new superpower constructions for metric generalized Jordan superpairs and revisits tensor product methods, expanding the algebraic toolkit for these structures.

Findings

Defined alternating and symmetric superpowers for metric generalized Jordan superpairs

Extended tensor product constructions via the Faulkner approach

Addressed characteristic constraints for nondegeneracy of bilinear forms

Abstract

The aim of this paper is to define and study the constructions of alternating and symmetric (super)powers of metric generalized Jordan (super)pairs. These constructions are obtained by transference via the Faulkner construction. The construction of tensor (super)products for metric generalized Jordan (super)pairs is revisited. We always assume that the characteristic of the base field $\mathbb{F}$ is different from $2$; in case of positive characteristic, sometimes we require that the characteristic is large enough to allow nondegeneracy of certain bilinear forms.