# superalgebra

A graded algebra $A$ is said to be a superalgebra if it has a $\mathbb{Z}/2\mathbb{Z}$ 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 $|ab|=|a|+|b|$.

 Title superalgebra Canonical name Superalgebra Date of creation 2013-03-22 12:46:18 Last modified on 2013-03-22 12:46:18 Owner mhale (572) Last modified by mhale (572) Numerical id 7 Author mhale (572) Entry type Definition Classification msc 16W55 Synonym super algebra Related topic Supernumber Related topic Supercommutative Related topic LieSuperalgebra Related topic LieSuperalgebra3 Related topic GradedAlgebra