Author(s)

Xue Chen

School of Applied Mathematics, Xiamen University of Technology, Xiamen, China.

The Nappi-Witten Lie algebra was first introduced by C. Nappi and E. Witten in the study of Wess-Zumino-Novikov-Witten (WZNW) models. They showed that the WZNW model (NW model) based on a central extension of the two-dimensional Euclidean group describes the homogeneous four-dimensional space-time corresponding to a gravitational plane wave. The associated Lie algebra is neither abelian nor semisimple. Recently K. Christodoulopoulou studied the irreducible Whittaker modules for finite- and infinite-dimensional Heisenberg algebras and for the Lie algebra obtained by adjoining a degree derivation to an infinite-dimensional Heisenberg algebra, and used these modules to construct a new class of modules for non-twisted affine algebras, which are called imaginary Whittaker modules. In this paper, imaginary Whittaker modules of the twisted affine Nappi-Witten Lie algebra are constructed based on Whittaker modules of Heisenberg algebras. It is proved that the imaginary Whittaker module with the center acting as a non-zero scalar is irreducible.

Twisted Affine Nappi-Witten Lie Algebras, Heisenberg Algebras, Imagi-nary Whittaker Modules

Chen, X. (2020) Imaginary Whittaker Modules of the Twisted Affine Nappi-Witten Lie Algebra . Journal of Applied Mathematics and Physics, 8, 548-554. doi: 10.4236/jamp.2020.83043.