Abstract
In this paper, we consider an integral basis for affine vertex algebra Vk (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 Vvir (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 Lav whose structure constants are integral to find an integral basis for the universal enveloping algebra of it.
Highlights
Vk when the level k is integral by a direct calculation, use the similar way to analyze an integral basis for Virasoro vertex algebra
We use the similar way to analyze an integral basis for Virasoso vertex algebra
We assume that the readers are familiar with the theory of vertex operator algebras [3] [6] [12] [13]
Summary
Among the most important vertex algebras are those associated with the Virasoro Lie algebra. It has been studied in [6] [7] [8]. We get an integral basis for the universal enveloping algebra of it. We observe that the -basis of affine vertex algebra Vk ( sl2 ) and Virasoro vertex algebra VVir (2k, 0) may be integral basis for them in certain conditions. We utilize the analogue of Chevalley bases for finite dimensional Lie algebras to get an integral basis for the universal enveloping algebra of affine-Virasoro algebra
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