On the non-abelian tensor product of Lie algebras

Salemkar, Ali Reza; Tavallaee, Hamid Agha; Mohammadzadeh, Hamid; Edalatzadeh, Behrouz

doi:10.1080/03081080802590834

Cited by 18 publications

(11 citation statements)

References 5 publications

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“…We note that the inequality in Theorem 4.2 can be found in [14] in the case of groups and has been recently adapted to Lie algebras in [16,Corollary 3.4]. Here, we are using a different argument in the proof and are able to characterize all those nilpotent Lie algebras which achieve the bound.…”

Section: Elamentioning

confidence: 86%

“…Applications to non-abelian tensor squares. In this section, we recall some constructions from [4,11,12,16] and illustrate the consequences of Theorems 3.1, 3.5 and 3.6 in a different context. Let F be a fixed field, L, K be two Lie algebras (not necessarily of finite dimen-…”

Section: In Theorems 31 and 35 We Proved Some Upper Bounds For Dim(mentioning

confidence: 99%

“…These are our main contributions, which are placed in Section 3, after we recall some fundamental tools in Section 2. Finally, an application is shown in Section 4, where the constructions in [4,11,12,16] are analyzed in virtue of the results in Section 3.…”

Section: Introduction and Terminology The Classification Of A Finitementioning

confidence: 99%

“…On another hand, [1,2,5,8,13,18] deal with bounds on dim(M (L)) and sometimes it is possible to adapt these bounds in order to study other important constructions of topology and K-theory, investigated in [4,11,12,16], where restrictions on the second homology group are involved.…”

Section: Introduction and Terminology The Classification Of A Finitementioning

confidence: 99%

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A restriction on the Schur multiplier of nilpotent Lie algebras

Niroomand¹,

Russo

2011

ELA

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Abstract. An improvement of a bound of Yankosky (2003) is presented in this paper, thanks to a restriction which has been recently obtained by the authors on the Schur multiplier M (L) of a finite dimensional nilpotent Lie algebra L. It is also described the structure of all nilpotent Lie algebras such that the bound is attained. An important role is played by the presence of a derived subalgebra of maximal dimension. This allows precision on the size of M (L). Among other results, applications to the non-abelian tensor square L ⊗ L are illustrated.

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Section: Elamentioning

confidence: 86%

Section: In Theorems 31 and 35 We Proved Some Upper Bounds For Dim(mentioning

confidence: 99%

Section: Introduction and Terminology The Classification Of A Finitementioning

confidence: 99%

Section: Introduction and Terminology The Classification Of A Finitementioning

confidence: 99%

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A restriction on the Schur multiplier of nilpotent Lie algebras

Niroomand¹,

Russo

2011

ELA

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“…The results from [20] on nilpotency, solvability and Engel of the non-abelian tensor product on Lie algebras can be easily extended to the case of Lie superalgebras. The notions of nilpotency and solvability of Lie superalgebras are given in [18].…”

Section: 2mentioning

confidence: 99%

Non-abelian tensor product and homology of Lie superalgebras

2015

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Available online xxxx Communicated by Volodymyr Mazorchuk MSC: 17B55 17B30 17B60 Keywords: Lie superalgebras Associative superalgebras Non-abelian tensor and exterior products Non-abelian homology Cyclic homology Hopf formula Crossed moduleWe introduce the non-abelian tensor product of Lie superalgebras and study some of its properties. We use it to describe the universal central extensions of Lie superalgebras. We present the low-dimensional non-abelian homology of Lie superalgebras and establish its relationship with the cyclic homology of associative superalgebras. We also define the non-abelian exterior product and give an analogue of Miller's theorem, Hopf formula and a six-term exact sequence for the homology of Lie superalgebras.

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