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

Abstract

Set $L≔H_4{\otimes }_{ℂ}R$ , $R≔ℂ\left[t^{\pm 1}\right]$ , and $S≔ℂ\left[t^{\pm 1/m}\right]\left(m\in {\mathbb{Z}}_{+}\right)$ . 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.