论文标题
关于nilpotent k-ary Lie代数的同源性
On the Homology of Nilpotent k-ary Lie Algebras
论文作者
论文摘要
我们介绍了Nilpotent K-Ary Lie代数，包括Heisenberg Lie代数和自由的Nilpotent Lie代数。我们通过使用Chevalley-Eilenberg综合体的修改来研究K- Ary Nilpotent Lie代数的同源。对于某些类别的nilpotent k-ary代数，尤其是海森伯格k-ary代数代数，我们为贝蒂数字提供了明确的公式。自由nilpotent k-ary lie代数的表示稳定性已被证明，贝蒂数字的下限由Schur模块描述。我们还验证了我们研究的课程的Toral Rank猜想是否存在。此外，对于两步的nilpotent k-ary lie代数，我们对其进行改进。
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.
