Abstract
Letgbe a finite dimensional semi-simple Lie algebra,U(g) its enveloping algebra, andHa finite subgroup ofAutU(g). LetAbe the invariant algebraUH. In this article, we prove that the Lie algebragis given (up to an isomorphism) by the algebraA. If we impose thatHis a finite subgroup of the adjoint group ofgacting on the enveloping algebraU(g), then the algebraAgives a unique group algebraC[H]. Ifg=sl2, then the groupHcan be recovered fromA.
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