Lie algebras with few centralizer dimensions
โ Scribed by Yiftach Barnea; I.M. Isaacs
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 171 KB
- Volume
- 259
- Category
- Article
- ISSN
- 0021-8693
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โฆ Synopsis
It is known that a finite group with just two different sizes of conjugacy classes must be nilpotent and it has recently been shown that its nilpotence class is at most 3. In this paper we study the analogs of these results for Lie algebras and some related questions.
๐ SIMILAR VOLUMES
By analogy with the definition of group with triality we introduce Lie algebra with triality as Lie algebra L which admits the group of automorphisms S 3 = {ฯ, ฯ | ฯ 2 = ฯ 3 = 1, ฯฯฯ = ฯ 2 } such that for any x โ L we have (x ฯx) + (x ฯx) ฯ + (x ฯx) ฯ 2 = 0. We describe the structure of finite-dimen
We present a combinatorial algorithm for computing dimensions of irreducible representations of all nine types of simple Lie algebras over complexes. We implemented it on a programmable desk calculator. In conclusion some physical applications are discussed. ## Various formulas have been given [1-3
We give a computer-free proof of the Deligne, Cohen and de Man formulas for the dimensions of the irreducible g-modules appearing in g k ; k44; where g ranges over the exceptional complex simple Lie algebras. We give additional dimension formulas for the exceptional series, as well as uniform dimens