The Schur multiplier and stem covers of Leibniz n-algebras

被引：1

作者：

Manuel Casas, Jose ^{[1
]}

Avelino Insua, Manuel ^{[1
]}

Pacheco Rego, Natalia ^{[2
,3
]}

机构：

[1] Univ Vigo, Dept Appl Math 1, EE Forestal, Pontevedra 36005, Spain

[2] Politech Inst Cavado, P-4750810 Vila Frescainha S Martin, Barcelos, Portugal

[3] Ave Campus IPCA, P-4750810 Vila Frescainha S Martin, Barcelos, Portugal

来源：

PUBLICATIONES MATHEMATICAE-DEBRECEN | 2019年 / 95卷 / 3-4期

关键词：

Leibniz n-algebra; Schur multiplier; stem cover; HOMOLOGY;

D O I：

10.5486/PMD.2019.8573

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a free presentation 0 -> R -> F ->(rho )G -> 0 of a Leibniz n-algebra G, the quotient R boolean AND[F, ...,F-n]/[R,F, ...(n-1), F] is known as the Schur multiplier of G. In the article, we construct a four-term exact sequence relating the Schur multiplier of G and G/N, from which we derive some formulas concerning dimensions of the underlying vector spaces of the corresponding Schur multipliers. Additionally, this exact sequence is useful to characterize nilpotency of Leibniz n-algebras. Finally, we characterize stem covers of Leibniz n-algebras, showing their existence in case of finite dimension. We also analyze the interaction between stem covers of Leibniz n-algebras and the Schur multiplier.

引用

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页码：437 / 468

页数：32

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