✦ LIBER ✦
A graph theoretical determination of solvable complete rigid Lie algebras
✍ Scribed by R Campoamor-Stursberg
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 132 KB
- Volume
- 372
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
We describe a class of nilpotent Lie algebras completely determined by their associated weight graph. These algebras also present two important structural properties: to admit naturally a symplectic form and to be isomorphic to the nilradical of a solvable complete rigid Lie algebra. These solvable algebras are proved to constitute a class of algebras where a symplectic form cannot exist. Finally we analyze the product by generators of the preceding algebras, and show that this operator preserves the property of being the maximal nilpotent ideal of a solvable rigid Lie algebra.