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Chapter 8 The Enveloping Algebra of a Semi-Simple Lie Algebra

1977; Elsevier BV; Linguagem: Inglês

10.1016/s0924-6509(08)70345-3

2212-0777

Advanced Algebra and Geometry

Publisher SummaryThis chapter determines the minimal primitive ideals of U(Ԥ) for an algebraically closed base field. r is assumed as the rank of Ԥ, ԥ a splitting Cartan subalgebra of Ԥ, R = R(Ԥ,ԥ), B a basis for R, and h the element of ԥ such that α(h) = 2 for all α ∈ B. If a is assumed as a Lie subalgebra of Ԥ, W a vector subspace of Ԥ such that Ԥ = a ⊕ W , and [a, W] ⊂ W; if adԤԤ and adԤa are assumed as the Lie algebras of irreducible algebraic groups Ң; and Ҝ, respectively; and if Ω is assumed as a Ң;-orbit, then the irreducible components of Ω ∩ α are Ҝ-orbits. The chapter also describes the enveloping algebra as a module over its centre and the adjoint representation in the enveloping algebra.