2019/10/16 by Stefano Marini, Marini, Stefano, Costantino Medori +3 · 1 citation
Mathematics · #17B22 #17B70 #53B05 #70G65 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1910.07896
openalex publication_date 2019/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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-Malčev 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.