nLab
super vector space

Context

Super-Algebra and Super-Geometry

Higher linear algebra

Contents

Idea

A super vector space is an object in the monoidal category SVect: as an object it is just a 2\mathbb{Z}_2-graded vector space, but when tensoring them one uses the non-trivial symmetric monoidal structure on 2\mathbb{Z}_2-graded vector spaces. In simple terms, this means that when switching two ‘odd’ vectors one introduces a minus sign:

vw(1) deg(v)deg(w)wv v \otimes w \mapsto (-1)^{deg(v) deg(w)} w \otimes v

References

Section 3.1 of

Revised on August 30, 2013 02:43:24 by Urs Schreiber (89.204.137.78)