𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Joint spectra and nilpotent lie algebras of linear transformations

✍ Scribed by Enrico Boasso

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
537 KB
Volume
263
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

Given a complex nilpotent finite dimensional Lie algebra of linear transformations, L, in a complex finite dimensional vector space, E, we study the joint spectra Sp(L, E), ,rs, k(L, E), and (r=, k(L , E). We compute them, and we prove that they all coincide with the set of weights of L for E. We also give a new interpretation of some basic module operations of the Lie algebra L in terms of the joint spectra.

πŸ“œ SIMILAR VOLUMES

On linear subspaces of nilpotent element
On linear subspaces of nilpotent elements in a Lie algebra
✍ Roy Meshulam; Nizar Radwan πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 235 KB

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 nil