Finitely and Freely Generated Lie Conformal Algebras.¶

AUTHORS:

Reimundo Heluani (2019-08-09): Initial implementation.

class sage.algebras.lie_conformal_algebras.finitely_freely_generated_lca.FinitelyFreelyGeneratedLCA(R, index_set=None, central_elements=None, category=None, element_class=None, prefix=None, names=None, latex_names=None, **kwds)[source]¶

Bases: FreelyGeneratedLieConformalAlgebra

Abstract base class for finitely generated Lie conformal algebras.

This class provides minimal functionality, simply sets the number of generators.

central_elements()[source]¶

The central elements of this Lie conformal algebra.

EXAMPLES:

Sage

sage: R = lie_conformal_algebras.NeveuSchwarz(QQ); R.central_elements()
(C,)

Python

>>> from sage.all import *
>>> R = lie_conformal_algebras.NeveuSchwarz(QQ); R.central_elements()
(C,)

gens()[source]¶

The generators for this Lie conformal algebra.

OUTPUT:

This method returns a tuple with the (finite) generators of this Lie conformal algebra.

EXAMPLES:

Sage

sage: Vir = lie_conformal_algebras.Virasoro(QQ);
sage: Vir.gens()
(L, C)

Python

>>> from sage.all import *
>>> Vir = lie_conformal_algebras.Virasoro(QQ);
>>> Vir.gens()
(L, C)

See also

lie_conformal_algebra_generators

ngens()[source]¶

The number of generators of this Lie conformal algebra.

EXAMPLES:

Sage

sage: Vir = lie_conformal_algebras.Virasoro(QQ); Vir.ngens()
2
sage: V = lie_conformal_algebras.Affine(QQ, 'A1'); V.ngens()
4

Python

>>> from sage.all import *
>>> Vir = lie_conformal_algebras.Virasoro(QQ); Vir.ngens()
2
>>> V = lie_conformal_algebras.Affine(QQ, 'A1'); V.ngens()
4