superalgebra

and

supergeometry

Contents

Idea

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

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

References

Section 3.1 of

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