Capability of Nilpotent Lie Algebras of Small Dimension

被引:2
|
作者
Shanbehbazari, Fatemeh Pazandeh [1 ]
Niroomand, Peyman [1 ]
Russo, Francesco G. [2 ]
Shamsaki, Afsaneh [1 ]
机构
[1] Univ Damghan, Sch Math & Comp Sci, Damghan, Iran
[2] Univ Cape Town, Dept Math & Appl Math, Private Bag X1, ZA-7701 Cape Town, South Africa
关键词
Nonabelian tensor square; Nonabelian exterior square; Capability; Schur multiplier; Lie algebras; SCHUR MULTIPLIER;
D O I
10.1007/s41980-021-00571-1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Given a nilpotent Lie algebra L of dimension <= 6 on an arbitrary field of characteristic not equal 2, we show a direct method to detect whether L is capable or not via computations on the size of its nonabelian exterior square L Lambda L. For dimensions higher than 6, we show a result of general nature, based on the evidences of the low dimensional case, but also on the evidences of large families of nilpotent Lie algebras, namely the generalized Heisenberg algebras. Indeed, we detect the capability of L Lambda L via the size of the Schur multiplier M(L/Z (Lambda) (L)) of L/Z(Lambda) (L), where Z(Lambda)(L) denotes the exterior center of L.
引用
收藏
页码:1153 / 1167
页数:15
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