superalgebra
A graded algebra is said to be a superalgebra if it has a grading.
As a vector space
, a superalgebra has a decomposition into two homogeneous
subspaces
, .
The homogeneous subspace is known as the space of even elements of , and is known as the space of odd elements.
Let denote the degree of a homogeneous element
.
That is, if and if .
The degree satisfies .
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 |