Abstract
Set L ≔ H 4 ⊗ ℂ R , R ≔ ℂ t ± 1 , and S ≔ ℂ t ± 1 / m m ∈ ℤ + . Then, L is called the loop Nappi–Witten Lie algebra. R -isomorphism classes of S / R forms of L are classified. The automorphism group and the derivation algebra of L are also characterized.
Highlights
E Nappi–Witten Lie algebra H4 is a four-dimensional Lie algebra over C generated by {a, b, c, d} with the following Lie brackets:
Reference [10] studied the automorphism groups of vertex operator algebras associated with the affine Nappi–Witten algebra H 4. e isomorphism of loop algebras was considered in [11] from the perspective of non-abelian Galois cohomology
Motivated by the works mentioned above, we study R-isomorphism classes of S/R forms of L, the automorphism group, and the derivation algebra of L in this paper
Summary
E Nappi–Witten Lie algebra H4 is a four-dimensional Lie algebra over C generated by {a, b, c, d} with the following Lie brackets:. En, L is a Lie algebra over C under the bracket as follows: Motivated by the works mentioned above, we study R-isomorphism classes of S/R forms of L, the automorphism group, and the derivation algebra of L in this paper. Lemma 3 (1) If (n, ξ, ρ, τ)2k (1, 0, 0, e) for k ∈ Z+, (n, ξ, ρ, τ) is conjugate to (1, 0, 0, τ) in Aut(H4).
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