Der Zentralisator einer Liealgebra in einer einhüllenden Algebra

Knop F (1990)

Publication Language: German

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 1990

Journal

Journal für die reine und angewandte Mathematik Walter de Gruyter

Publisher: Walter de Gruyter

Book Volume: 406

Pages Range: 5-9

Abstract

Let g be a complex semisimple Lie algebra and k a reductive subalgebra of g. The paper is concerned with the centralizer U(g)^k of k in the enveloping algebra U(g). Denote by z(g), z(k) the center of U(g), U(k) respectively. Then there is a canonical homomorphism p:z(g)\otimes z(k)-->U(g)^k.

Theorem: Assume k does not contain a non-zero ideal of g. Then the following statements are equivalent:

  1. p is an isomorphism;
  2. U(g)^k is commutative;
  3. the pair (g,k) is either (sl(n), gl(n-1)) n>=2 or (so(n), so(n-1)) n>=4.

The method is using the canonical filtration of U(g) and then proving an equivalent theorem for the associated graded algebra.

Authors with CRIS profile

Friedrich Knop Lehrstuhl für Mathematik (Algebra und Geometrie)

How to cite

APA:

Knop, F. (1990). Der Zentralisator einer Liealgebra in einer einhüllenden Algebra. Journal für die reine und angewandte Mathematik, 406, 5-9.

MLA:

Knop, Friedrich. "Der Zentralisator einer Liealgebra in einer einhüllenden Algebra." Journal für die reine und angewandte Mathematik 406 (1990): 5-9.

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