## Supersymmetry classes of tensors

### Volume 120 / 2010

Colloquium Mathematicum 120 (2010), 267-275
MSC: Primary 15A69; Secondary 20C15.
DOI: 10.4064/cm120-2-7

#### Abstract

We introduce the notion of a *supersymmetry class
of tensors* which is the ordinary symmetry class of tensors
with a natural ${\mathbb Z}_2$-gradation. We give the
dimensions of *even* and *odd* parts of this gradation as well as
their natural bases. Also
we give a necessary and sufficient condition for the odd or even part of a supersymmetry class to be zero.