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On linear subspaces of nilpotent elements in a Lie algebra

✍ Scribed by Roy Meshulam; Nizar Radwan

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
235 KB
Volume
279
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let 9 be a complex semi-simple Lie algebra. Extending a result of Gerstenhaber on spaces of nilpotent matrices, it is shown that if W c g is a linear subspace of ad nilpotent elements then dim W < i( dim.g -rank g). Similarly, it is shown that the maximal dimension of a linear space of symmetric nilpotent n x n complex matrices is Lanz].

πŸ“œ SIMILAR VOLUMES

A Proof of Hozo's Conjecture on the Homo
A Proof of Hozo's Conjecture on the Homology of a Class of Nilpotent Lie Algebras
✍ Phil Hanlon πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 342 KB

a poset by saying u F Β¨if u is on the path from r to Β¨. Let Z P be the span of all matrices z such that u -Β¨, where z is the n = n matrix with a 1 in the u, ΓΌΒ¨P u αΊ… x Ε½ .