Neveu-Schwarz Super Lie Conformal Algebra¶
The \(N=1\) or Neveu-Schwarz super Lie conformal algebra is a super extension of the Virasoro Lie conformal algebra with generators \(L\) and \(C\) by an odd primary generator \(G\) of conformal weight \(3/2\). The remaining \(\lambda\)-bracket is given by:
\[[G_\lambda G] = 2L + \frac{\lambda^2}{3} C.\]
AUTHORS:
Reimundo Heluani (2020-06-03): Initial implementation.
- class sage.algebras.lie_conformal_algebras.neveu_schwarz_lie_conformal_algebra.NeveuSchwarzLieConformalAlgebra(R)¶
Bases:
sage.algebras.lie_conformal_algebras.graded_lie_conformal_algebra.GradedLieConformalAlgebra
The Neveu-Schwarz super Lie conformal algebra.
INPUT:
R
– a commutative Ring; the base ring of this Lie conformal algebra.
EXAMPLES:
sage: R = lie_conformal_algebras.NeveuSchwarz(AA); R The Neveu-Schwarz super Lie conformal algebra over Algebraic Real Field sage: R.structure_coefficients() Finite family {('G', 'G'): ((0, 2*L), (2, 2/3*C)), ('G', 'L'): ((0, 1/2*TG), (1, 3/2*G)), ('L', 'G'): ((0, TG), (1, 3/2*G)), ('L', 'L'): ((0, TL), (1, 2*L), (3, 1/2*C))} sage: R.inject_variables() Defining L, G, C sage: G.nproduct(G,0) 2*L sage: G.degree() 3/2