super vector space

and

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:

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

Section 3.1 of

- Veeravalli Varadarajan,
*Supersymmetry for mathematicians: An introduction*, Courant lecture notes in mathematics, American Mathematical Society Providence, R.I 2004

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