# 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)

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}