Lefschetz fibrations, Lie groupoids and noncommutative geometry
The Lie algebra of derivations on a polynomial ring and certain maximal subalgebras
Global geometry of singular holomorphic foliations and distributions
| Full text | |
| Author(s): |
Conti, D.
;
del Barco, V.
;
Rossi, F. A.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. N/A, p. 26-pg., 2024-04-05. |
| Abstract | |
We proved in previous work that all real nilpotent Lie algebras of dimension up to 10 carrying an ad-invariant metric are nice, i.e. they admit a nice basis in the sense of Lauret et al. In this paper, we show by constructing explicit examples that nonnice irreducible nilpotent Lie algebras admitting an ad-invariant metric exist for every dimension greater than 10 and every nilpotency step greater than 2. In the way of doing so, we introduce a method to construct Lie algebras with ad-invariant metrics called the single extension, as a parallel to the well-known double extension procedure. (AU) | |
| FAPESP's process: | 21/09197-8 - Special invariant metrics on Lie groups and their compact quotients |
| Grantee: | Viviana Jorgelina Del Barco |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 23/15089-9 - Aspects of the conformal and Riemannian geometry of Lie groups and their compact quotients. |
| Grantee: | Viviana Jorgelina Del Barco |
| Support Opportunities: | Regular Research Grants |