On some classes of Z-graded Lie algebras
Differential Geometry
2019-10-18 v1
Abstract
We study finite dimensional almost and quasi-effective prolongations of nilpotent Z-graded Lie algebras, especially focusing on those having a decomposable reductive structural subalgebra. Our assumptions generalize effectiveness and algebraicity and are appropriate to obtain Levi-Mal\v{c}ev and Levi-Chevalley decompositions and precisions on the heigth and other properties of the prolongations in a very natural way. In a last section we systematically present examples in which simple Lie algebras are obtained as prolongations, for reductive structural algebras of type A, B, C and D, of nilpotent Z-graded Lie algebras arising as their linear representations.
Keywords
Cite
@article{arxiv.1910.07896,
title = {On some classes of Z-graded Lie algebras},
author = {Stefano Marini and Costantino Medori and Mauro Nacinovich},
journal= {arXiv preprint arXiv:1910.07896},
year = {2019}
}
Comments
35 pages. arXiv admin note: text overlap with arXiv:1806.09376