Automorphisms and derivations of Borel subalgebras and their nilradicals in Kac-Moody algebras

Details Automorphisms and derivations of Borel subalgebras and their nilradicals in Kac-Moody algebras Automorphisms and derivations of Borel subalgebras and their nilradicals in Kac-Moody algebras

2008-06-30

arxiv.org/abs/0806.4922v1

Mathematics

Rings and Algebras

Scientific paper

In this paper, we determine derivations of Borel subalgebras and their derived subalgebras called nilradicals, in Kac-Moody algebras (and contragredient Lie algebras) over any field of characteristic 0; and we also determine automorphisms of those subalgebras in symmetrizable Kac-Moody algebras. The results solve a conjecture posed by R. V. Moody about 30 years ago which generalizes a result by B. Kostant and which is discussed by A. Fialowski using Lie algebra cohomology in case of affine type.

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