Super Lie Conformal Algebras#
AUTHORS:
Reimundo Heluani (2019-10-05): Initial implementation.
- class sage.categories.super_lie_conformal_algebras.SuperLieConformalAlgebras(base_category)#
Bases:
SuperModulesCategory
The category of super Lie conformal algebras.
EXAMPLES:
sage: LieConformalAlgebras(AA).Super() # optional - 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',), # optional - sage.combinat sage.modules ....: central_elements=('K',), super=True) sage: [g.is_even_odd() for g in R.gens()] # optional - sage.combinat sage.modules [0, 0]
- class ElementMethods#
Bases:
object
- is_even_odd()#
Return
0
if this element is even and1
if it is odd.EXAMPLES:
sage: R = lie_conformal_algebras.NeveuSchwarz(QQ) # optional - sage.combinat sage.modules sage: R.inject_variables() # optional - sage.combinat sage.modules Defining L, G, C sage: G.is_even_odd() # optional - sage.combinat sage.modules 1
- class Graded(base_category)#
Bases:
GradedModulesCategory
The category of H-graded super Lie conformal algebras.
EXAMPLES:
sage: LieConformalAlgebras(AA).Super().Graded() # optional - sage.rings.number_field Category of H-graded super Lie conformal algebras over Algebraic Real Field
- class ParentMethods#
Bases:
object
- example()#
An example parent in this category.
EXAMPLES:
sage: LieConformalAlgebras(QQ).Super().example() # optional - sage.combinat sage.modules The Neveu-Schwarz super Lie conformal algebra over Rational Field
- 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]