Super Lie Conformal Algebras¶
AUTHORS:
- Reimundo Heluani (2019-10-05): Initial implementation. 
- class sage.categories.super_lie_conformal_algebras.SuperLieConformalAlgebras(base_category)[source]¶
- Bases: - SuperModulesCategory- The category of super Lie conformal algebras. - EXAMPLES: - sage: LieConformalAlgebras(AA).Super() # needs sage.rings.number_field Category of super Lie conformal algebras over Algebraic Real Field - >>> from sage.all import * >>> LieConformalAlgebras(AA).Super() # needs sage.rings.number_field 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',), # needs sage.combinat sage.modules ....: central_elements=('K',), super=True) sage: [g.is_even_odd() for g in R.gens()] # needs sage.combinat sage.modules [0, 0] - >>> from sage.all import * >>> bosondict = {('a','a'): {Integer(1):{('K',Integer(0)):Integer(1)}}} >>> R = LieConformalAlgebra(QQ, bosondict, names=('a',), # needs sage.combinat sage.modules ... central_elements=('K',), super=True) >>> [g.is_even_odd() for g in R.gens()] # needs sage.combinat sage.modules [0, 0] - class ElementMethods[source]¶
- Bases: - object- is_even_odd()[source]¶
- Return - 0if this element is even and- 1if it is odd.- EXAMPLES: - sage: R = lie_conformal_algebras.NeveuSchwarz(QQ) # needs sage.combinat sage.modules sage: R.inject_variables() # needs sage.combinat sage.modules Defining L, G, C sage: G.is_even_odd() # needs sage.combinat sage.modules 1 - >>> from sage.all import * >>> R = lie_conformal_algebras.NeveuSchwarz(QQ) # needs sage.combinat sage.modules >>> R.inject_variables() # needs sage.combinat sage.modules Defining L, G, C >>> G.is_even_odd() # needs sage.combinat sage.modules 1 
 
 - class Graded(base_category)[source]¶
- Bases: - GradedModulesCategory- The category of H-graded super Lie conformal algebras. - EXAMPLES: - sage: LieConformalAlgebras(AA).Super().Graded() # needs sage.rings.number_field Category of H-graded super Lie conformal algebras over Algebraic Real Field - >>> from sage.all import * >>> LieConformalAlgebras(AA).Super().Graded() # needs sage.rings.number_field Category of H-graded super Lie conformal algebras over Algebraic Real Field 
 - example()[source]¶
- An example parent in this category. - EXAMPLES: - sage: LieConformalAlgebras(QQ).Super().example() # needs sage.combinat sage.modules The Neveu-Schwarz super Lie conformal algebra over Rational Field - >>> from sage.all import * >>> LieConformalAlgebras(QQ).Super().example() # needs sage.combinat sage.modules The Neveu-Schwarz super Lie conformal algebra over Rational Field 
 - extra_super_categories()[source]¶
- 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] - >>> from sage.all import * >>> LieConformalAlgebras(QQ).Super().super_categories() [Category of super modules over Rational Field, Category of Lambda bracket algebras over Rational Field]