superalgebra

A graded algebra $A$ is said to be a superalgebra if it has a $\Zset/2\Zset$ grading. As a vector space, a superalgebra has a decomposition into two homogeneous subspaces, $A = A_0\oplus A_1$ . The homogeneous subspace $A_0$ is known as the space of even elements of $A$ , and $A_1$ is known as the space of odd elements. Let $|a|$ denote the degree of a homogeneous element. That is, $|a| = 0$ if $a \in A_0$ and $|a| = 1$ if $a \in A_1$ . The degree satisfies $|ab| = |a| + |b|$ .