Virasoro Lie Conformal Algebra - Algebras

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# 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: `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

      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}

  Python

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