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Highest-weight theory for truncated current Lie algebras

2011; Elsevier BV; Volume: 336; Issue: 1 Linguagem: Inglês

10.1016/j.jalgebra.2011.04.015

1090-266X

Benjamin J. Wilson,

Advanced Algebra and Geometry

In this paper a highest-weight theory for the truncated current Lie algebra gˆgˆ=g⊗kk[t]/tN+1k[t] is developed when the underlying Lie algebra g possesses a triangular decomposition. The principal result is the reducibility criterion for the Verma modules of gˆ for a wide class of Lie algebras g, including the symmetrizable Kac–Moody Lie algebras, the Heisenberg algebra, and the Virasoro algebra. This is achieved through a study of the Shapovalov form.