（扭）仿射Nappi-Witten李代数与Hom-李代数的结构和表示理论

（扭）仿射Nappi-Witten李代数来源于建立在非半单李群上的WZNW模型，Hom-李代数是经典李代数的推广，因此研究这两类代数的结构及表示理论在物理和数学领域都具有重要意义。本项目我们拟对（扭）仿射Nappi-Witten李代数的表示与Hom-李代数的结构及表示展开研究。研究内容包括（扭）仿射Nappi-Witten李代数的Verma-型模、顶点算子表示、Wakimoto模、（虚拟）Whittaker模、李双代数与Hom-李代数的结构及表示。

Since (twisted) affine Nappi-Witten Lie algebras are from WZNW models based on nonsemisimple Lie groups and Hom-Lie algebras are generalization of classical Lie algebras, it has important significance in physics and mathematics to study the structures and representations of the two algebras. We plan to study the representations of (twisted) affine Nappi-Witten Lie algebras and the structures and representations of Hom-Lie algebras. The research contents include Verma-type modules, vertex operator representations, Wakimoto modules, (imaginary) Whittaker modules for (twisted) affine Nappi-Witten Lie algebras and the structures and representations of Hom-Lie algebras.