Virasoro Lie Conformal Algebra#

The Virasoro Lie conformal algebra is generated by \(L\) and a central element \(C\). The \(\lambda\)-brackets are given by:

\[[L_\lambda L] = T L + 2 \lambda L + \frac{\lambda^3}{12} C.\]

It is an H-graded Lie conformal algebra with \(L\) of degree \(2\).

AUTHORS:

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

class sage.algebras.lie_conformal_algebras.virasoro_lie_conformal_algebra.VirasoroLieConformalAlgebra(R)#

Bases: sage.algebras.lie_conformal_algebras.graded_lie_conformal_algebra.GradedLieConformalAlgebra

The Virasoro Lie Conformal algebra over \(R\).

INPUT:

  • R – a commutative ring; behaviour is undefined if \(R\) is not a Field of characteristic zero.

EXAMPLES:

sage: Vir = lie_conformal_algebras.Virasoro(QQ)
sage: Vir.category()
Category of H-graded finitely generated Lie conformal algebras with basis over Rational Field
sage: Vir.inject_variables()
Defining L, C
sage: L.bracket(L)
{0: TL, 1: 2*L, 3: 1/2*C}