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)[source]¶
- 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: 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} - >>> 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}