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superalgebra (Definition)

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




"superalgebra" is owned by mhale. [ full author list (2) | owner history (1) ]
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See Also: supernumber, supercommutative, Lie super algebra, Lie superalgebra, graded algebra

Other names:  super algebra
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Cross-references: homogeneous element, degree, odd, even, subspaces, homogeneous, decomposition, vector space, grading, graded algebra
There are 15 references to this entry.

This is version 4 of superalgebra, born on 2002-06-09, modified 2007-12-17.
Object id is 3082, canonical name is SuperAlgebra.
Accessed 5434 times total.

Classification:
AMS MSC16W55 (Associative rings and algebras :: Rings and algebras with additional structure :: ``Super'' structure)

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