Super Lie Conformal Algebras¶
AUTHORS:
Reimundo Heluani (2019-10-05): Initial implementation.
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class
sage.categories.super_lie_conformal_algebras.
SuperLieConformalAlgebras
(base_category)¶ Bases:
sage.categories.super_modules.SuperModulesCategory
The category of super Lie conformal algebras.
EXAMPLES:
sage: LieConformalAlgebras(AA).Super() Category of super Lie conformal algebras over Algebraic Real Field
Notice that we can force to have a purely even super Lie conformal algebra:
sage: bosondict = {('a','a'):{1:{('K',0):1}}} sage: R = LieConformalAlgebra(QQ,bosondict,names=('a',), ....: central_elements=('K',), super=True) sage: [g.is_even_odd() for g in R.gens()] [0, 0]
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class
ElementMethods
¶ Bases:
object
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is_even_odd
()¶ Return
0
if this element is even and1
if it is odd.EXAMPLES:
sage: R = lie_conformal_algebras.NeveuSchwarz(QQ); sage: R.inject_variables() Defining L, G, C sage: G.is_even_odd() 1
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class
Graded
(base_category)¶ Bases:
sage.categories.graded_modules.GradedModulesCategory
The category of H-graded super Lie conformal algebras.
EXAMPLES:
sage: LieConformalAlgebras(AA).Super().Graded() Category of H-graded super Lie conformal algebras over Algebraic Real Field
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class
ParentMethods
¶ Bases:
object
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example
()¶ An example parent in this category.
EXAMPLES:
sage: LieConformalAlgebras(QQ).Super().example() The Neveu-Schwarz super Lie conformal algebra over Rational Field
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extra_super_categories
()¶ The extra super categories of
self
.EXAMPLES:
sage: LieConformalAlgebras(QQ).Super().super_categories() [Category of super modules over Rational Field, Category of Lambda bracket algebras over Rational Field]
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class