Nilpotent Lie Algebras of Maximal Rank and of Kac–Moody Type: E6(1)
✍ Scribed by D. Fernández-Ternero; J. Núñez-Valdés
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 271 KB
- Volume
- 250
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
The first family of Kac-Moody Lie algebras studied are the simple Lie algebras. The study of nilpotent Lie algebras of maximal rank and of type A B C D was made by Favre and Santharoubane in [5]. Later, Agrafiotou and Tsagas studied these algebras, of types E 6 E 7 , and E 8 finding that there exist (up to isomorphism) 149 nilpotent Lie algebras of maximal rank and of type E 6 and 1605 nilpotent Lie algebras of maximal rank and of type E 7 (see [3]). Favre and Tsagas studied the nilpotent Lie algebras of maximal rank and of type F 4 (see [6]).
The second family of Kac-Moody algebras are the affine Lie algebras. Santharoubane studied in 1982 (see [12]) the affine Lie algebras of rank 2 and of types A 1 1 and A 2 2 . He proved that there are exactly (up to isomorphism), three infinite series and 10 infinite series, respectively, of nilpotent Lie algebras of maximal rank such that A 1 1 and A 2 2 are Cartan matrices associated. Kanagavel studied in [10] the nontwisted affine Lie algebras, of rank 3 and of types A 1 2 B 1 2 , and G 1 2 . He proved that there are exactly n X infinite series and a continuous family of nilpotent Lie algebras of maximal rank and of type X, where n A