A generalization of Veldkamp's theorem for a class of Lie algebras

Abstract

A classical theorem of Veldkamp describes the center of an enveloping algebra of a Lie algebra of a semi-simple algebraic group in characteristic $p.$ We generalize this result to a class of Lie algebras with a property that they arise as the reduction modulo $p\gg 0$ from an algebraic Lie algebra $\mathfrak{g},$ such that $\mathfrak{g}$ has no nontrivial semi-invariants in $Sym(\mathfrak{g})$ and $Sym(\mathfrak{g}{)}^{\mathfrak{g}}$ is a polynomial algebra. As an application, we solve the derived isomorphism problem of enveloping algebras for the above class of Lie algebras.

Significantly revised, final version. To appear in Journal of Algebra

References in corpus (2)

• Invariant polynomials on truncated multicurrent algebras
• The polynomiality of the Poisson center and semi-center of a Lie algebra and Dixmier's fourth problem