A Lie algebra can be considered as a Lie superalgebra by setting and, therefore, .
The Lie superbracket (2) is called the supercommutator bracket on .
The space of graded derivations of a supercommutative superalgebra, equipped with the supercommutator bracket, is a Lie superalgebra.
A vector superspace is a vector space equipped with a decomposition .
Let be a vector superspace. Then any element of is said to be even, and any element of is said to be odd. By the definition of the direct sum, any element of can be uniquely written as , where and .
A vector is homogeneous of degree if for or .
If is homogeneous, then the degree of is denoted by . In other words, if , then by definition.
The vector is homogeneous of both degree and , and thus is not well-defined.
|Date of creation||2013-03-22 15:35:44|
|Last modified on||2013-03-22 15:35:44|
|Last modified by||bci1 (20947)|
|Synonym||Lie super algebra|
|Synonym||graded Lie algebra|