nLab
supercommutative algebra

Contents

Idea

A super-commutative algebra is a commutative algebra internal to the symmetric monoidal category of super vector spaces, hence a /2\mathbb{Z}/2-graded associative algebra such that for a,ba, b any two elements of homogeneous degree deg(a),deg(b)/2={0,1}deg(a), deg(b) \in \mathbb{Z}/2 = \{0,1\}, then

ab=(1) deg(a)deg(b)ba. a b = (-1)^{deg(a) deg(b)} b a \,.

For more see at geometry of physics – superalgebra.

Examples

Last revised on April 8, 2018 at 12:51:32. See the history of this page for a list of all contributions to it.