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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.

The Classification, Automorphism Group, and Derivation Algebra of the Loop Algebra Related to the Nappi–Witten Lie Algebra