Freely Generated Lie Conformal Algebras

AUTHORS:

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

class sage.algebras.lie_conformal_algebras.freely_generated_lie_conformal_algebra.FreelyGeneratedLieConformalAlgebra(R, index_set=None, central_elements=None, category=None, element_class=None, prefix=None, **kwds)

Bases: LieConformalAlgebraWithBasis

Base class for a central extension of a freely generated Lie conformal algebra.

This class provides minimal functionality, it sets up the family of Lie conformal algebra generators.

Note

We now only accept direct sums of free modules plus some central generators \(C_i\) such that \(TC_i = 0\).

central_elements()

The central generators of this Lie conformal algebra.

EXAMPLES:

sage: Vir = lie_conformal_algebras.Virasoro(QQ)
sage: Vir.central_elements()
(C,)
sage: V = lie_conformal_algebras.Affine(QQ, 'A1')
sage: V.central_elements()
(B['K'],)

lie_conformal_algebra_generators()

The generators of this Lie conformal algebra.

OUTPUT: a (possibly infinite) family of generators (as an \(R[T]\)-module) of this Lie conformal algebra.

EXAMPLES:

sage: Vir = lie_conformal_algebras.Virasoro(QQ)
sage: Vir.lie_conformal_algebra_generators()
(L, C)
sage: V = lie_conformal_algebras.Affine(QQ,'A1')
sage: V.lie_conformal_algebra_generators()
(B[alpha[1]], B[alphacheck[1]], B[-alpha[1]], B['K'])