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 methodcartan_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']}
- either an attribute