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