A graded algebraMathworldPlanetmath A is said to be a superalgebra if it has a /2 grading. As a vector spaceMathworldPlanetmath, a superalgebra has a decomposition into two homogeneousPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath subspacesMathworldPlanetmathPlanetmath, A=A0A1. The homogeneous subspace A0 is known as the space of even elements of A, and A1 is known as the space of odd elements. Let |a| denote the degree of a homogeneous elementPlanetmathPlanetmath. That is, |a|=0 if aA0 and |a|=1 if aA1. 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