On the Homology of Nilpotent k-ary Lie Algebras

Autor:	Sen, Emre
Rok vydání:	2020
Předmět:	Mathematics - Representation Theory Mathematics - Combinatorics Mathematics - Rings and Algebras 17B30 17B55 17B56 05E15
Druh dokumentu:	Working Paper
Popis:	We introduce nilpotent k-ary Lie algebras including analogues of Heisenberg Lie algebras and free nilpotent Lie algebras. We study homology of k-ary nilpotent Lie algebras by using a modification of Chevalley-Eilenberg complex. For some classes of nilpotent k-ary Lie algebras and in particular Heisenberg k-ary Lie algebras we give explicit formulas for Betti numbers. Representation stability of free nilpotent k-ary Lie algebras is proven and lower bounds for Betti numbers are described by Schur modules. We also verify that toral rank conjecture holds for the classes we studied. Moreover, for 2-step nilpotent k-ary Lie algebras, we give a refinement of it. Comment: Comments are wellcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2006.03794 Zobrazit plný text záznamu View this record from Arxiv