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)[source]¶
- 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()[source]¶
- 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'],) - >>> from sage.all import * >>> Vir = lie_conformal_algebras.Virasoro(QQ) >>> Vir.central_elements() (C,) >>> V = lie_conformal_algebras.Affine(QQ, 'A1') >>> V.central_elements() (B['K'],) 
 - lie_conformal_algebra_generators()[source]¶
- 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']) - >>> from sage.all import * >>> Vir = lie_conformal_algebras.Virasoro(QQ) >>> Vir.lie_conformal_algebra_generators() (L, C) >>> V = lie_conformal_algebras.Affine(QQ,'A1') >>> V.lie_conformal_algebra_generators() (B[alpha[1]], B[alphacheck[1]], B[-alpha[1]], B['K'])