Supercommutative Algebras¶
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class
sage.categories.supercommutative_algebras.
SupercommutativeAlgebras
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_over_base_ring
The category of supercommutative algebras.
An \(R\)-supercommutative algebra is an \(R\)-super algebra \(A = A_0 \oplus A_1\) endowed with an \(R\)-super algebra structure satisfying:
\[x_0 x'_0 = x'_0 x_0, \qquad x_1 x'_1 = -x'_1 x_1, \qquad x_0 x_1 = x_1 x_0,\]for all \(x_0, x'_0 \in A_0\) and \(x_1, x'_1 \in A_1\).
EXAMPLES:
sage: Algebras(ZZ).Supercommutative() Category of supercommutative algebras over Integer Ring
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class
SignedTensorProducts
(category, *args)¶ Bases:
sage.categories.signed_tensor.SignedTensorProductsCategory
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extra_super_categories
()¶ Return the extra super categories of
self
.A signed tensor product of supercommutative algebras is a supercommutative algebra.
EXAMPLES:
sage: C = Algebras(ZZ).Supercommutative().SignedTensorProducts() sage: C.extra_super_categories() [Category of supercommutative algebras over Integer Ring]
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class
WithBasis
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_over_base_ring
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class
ParentMethods
¶ Bases:
object
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class
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class