Regular Supercrystals

sage.categories.regular_supercrystals.RegularSuperCrystals

The category of crystals for super Lie algebras.

EXAMPLES:

sage: from sage.categories.regular_supercrystals import RegularSuperCrystals
sage: C = RegularSuperCrystals()
sage: C
Category of regular super crystals
sage: C.super_categories()
[Category of finite crystals]

Parents in this category should implement the following methods:

  • either an attribute _cartan_type or a method cartan_type
  • module_generators: a list (or container) of distinct elements that generate the crystal using \(f_i\) and \(e_i\)

Furthermore, their elements x should implement the following methods:

  • x.e(i) (returning \(e_i(x)\))
  • x.f(i) (returning \(f_i(x)\))
  • x.weight() (returning \(\operatorname{wt}(x)\))

EXAMPLES:

sage: from sage.misc.abstract_method import abstract_methods_of_class
sage: from sage.categories.regular_supercrystals import RegularSuperCrystals
sage: abstract_methods_of_class(RegularSuperCrystals().element_class)
{'optional': [], 'required': ['e', 'f', 'weight']}