Author(s)

Ashuai Wang

School of Mathematics, South China University of Technology, Guangzhou, China.

In this paper, we consider an integral basis for affine vertex algebra V_k (sl₂) when the level k is integral by a direct calculation, then use the similar way to analyze an integral basis for Virasoro vertex algebra V_vir (2k,0). Finally, we take the combination of affine algebras and Virasoro Lie algebras into consideration. By analogy with the construction of Lie algebras over Z using Chevalley bases, we utilize the Z-basis of L_av whose structure constants are integral to find an integral basis for the universal enveloping algebra of it.

Vertex algebra, Integral Basis, Virasoro Algebra, Affine Algebra

Wang, A. (2020) Integral Basis of Affine Vertex Algebra V_k (sl₂) and Virasoro Vertex Algebra V_vir (2k,0). Journal of Applied Mathematics and Physics, 8, 652-659. doi: 10.4236/jamp.2020.84050.