The schur multiplier of a nilpotent Lie algebra with derived subalgebra of maximum dimension

2020 ◽  
pp. 1-8
Author(s):  
Farangis Johari ◽  
Peyman Niroomand ◽  
Afsaneh Shamsaki
Keyword(s):  
Lie Algebra ◽  
Schur Multiplier ◽  
Nilpotent Lie Algebra ◽  
Maximum Dimension

scholarly journals Certain functors of nilpotent Lie algebras with the derived subalgebra of dimension two

2019 ◽  
Vol 19 (01) ◽  
pp. 2050012
Author(s):  
Farangis Johari ◽  
Peyman Niroomand
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Schur Multiplier ◽  
Nilpotent Lie Algebra ◽  
Nilpotent Lie Algebras ◽  
Dimension Formula ◽  
Tensor Square ◽  
Exterior Square

By considering the nilpotent Lie algebra with the derived subalgebra of dimension [Formula: see text], we compute some functors including the Schur multiplier, the exterior square and the tensor square of these Lie algebras. We also give the corank of such Lie algebras.

scholarly journals A Note on the Schur Multiplier of a Nilpotent Lie Algebra

2011 ◽  
Vol 39 (4) ◽  
pp. 1293-1297 ◽  
Author(s):  
Peyman Niroomand ◽  
Francesco G. Russo
Keyword(s):  
Lie Algebra ◽  
Schur Multiplier ◽  
Nilpotent Lie Algebra

On dimension of Schur multiplier of nilpotent Lie algebras II

2017 ◽  
Vol 10 (04) ◽  
pp. 1750076 ◽  
Author(s):  
F. Saeedi ◽  
H. Arabyani ◽  
P. Niroomand
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Heisenberg Algebra ◽  
Schur Multiplier ◽  
Nilpotent Lie Algebra ◽  
Nilpotent Lie Algebras ◽  
Dimension Formula

Let [Formula: see text] be a non-abelian nilpotent Lie algebra of dimension [Formula: see text] and put [Formula: see text], where [Formula: see text] denotes the Schur multiplier of [Formula: see text]. Niroomand and Russo in 2011 proved that [Formula: see text] and that [Formula: see text] if and only if [Formula: see text], in which [Formula: see text] is the Heisenberg algebra of dimension [Formula: see text] and [Formula: see text] is the abelian [Formula: see text]-dimensional Lie algebra. In the same year, they also classified all nilpotent Lie algebras [Formula: see text] satisfying [Formula: see text] or [Formula: see text]. In this paper, we obtain all nilpotent Lie algebras [Formula: see text] provided that [Formula: see text].

On the capability and Schur multiplier of nilpotent Lie algebra of class two

2016 ◽  
Vol 144 (10) ◽  
pp. 4157-4168 ◽  
Author(s):  
Peyman Niroomand ◽  
Farangis Johari ◽  
Mohsen Parvizi
Keyword(s):  
Lie Algebra ◽  
Schur Multiplier ◽  
Nilpotent Lie Algebra

scholarly journals The Schur multipliers of Lie algebras of maximal class

2019 ◽  
Vol 29 (05) ◽  
pp. 795-801
Author(s):  
Afsaneh Shamsaki ◽  
Peyman Niroomand
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Maximal Class ◽  
Schur Multiplier ◽  
Nilpotent Lie Algebra ◽  
Nilpotent Lie Algebras ◽  
Schur Multipliers ◽  
Dimension Formula

Let [Formula: see text] be a non-abelian nilpotent Lie algebra of dimension [Formula: see text] and [Formula: see text] be its Schur multiplier. It was proved by the second author the dimension of the Schur multiplier is equal to [Formula: see text] for some [Formula: see text]. In this paper, we classify all nilpotent Lie algebras of maximal class for [Formula: see text]. The dimension of Schur multiplier of such Lie algebras is also bounded by [Formula: see text]. Here, we give the structure of all nilpotent Lie algebras of maximal class [Formula: see text] when [Formula: see text] and then we show that all of them are capable.

On Automorphisms and Derivations of a Lie Algebra

2006 ◽  
Vol 13 (01) ◽  
pp. 119-132 ◽  
Author(s):  
V. R. Varea ◽  
J. J. Varea
Keyword(s):  
Automorphism Group ◽  
Normal Subgroup ◽  
Large Class ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Finite Dimension ◽  
Nilpotent Lie Algebra ◽  
Identity Component ◽  
Trivial Center

We study automorphisms and derivations of a Lie algebra L of finite dimension satisfying certain centrality conditions. As a consequence, we obtain that every nilpotent normal subgroup of the automorphism group of L is unipotent for a very large class of Lie algebras. This result extends one of Leger and Luks. We show that the automorphism group of a nilpotent Lie algebra can have trivial center and have yet a unipotent identity component.

Some studies on central derivation of nilpotent Lie superalgebra

2018 ◽  
Vol 13 (04) ◽  
pp. 2050068
Author(s):  
Rudra Narayan Padhan ◽  
K. C. Pati
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Nilpotent Lie Algebra ◽  
New Concepts

Many theorems and formulas of Lie superalgebras run quite parallel to Lie algebras, sometimes giving interesting results. So it is quite natural to extend the new concepts of Lie algebra immediately to Lie superalgebra case as the later type of algebras have wide applications in physics and related theories. Using the concept of isoclinism, Saeedi and Sheikh-Mohseni [A characterization of stem algebras in terms of central derivations, Algebr. Represent. Theory 20 (2017) 1143–1150; On [Formula: see text]-derivations of Filippov algebra, to appear in Asian-Eur. J. Math.; S. Sheikh-Mohseni, F. Saeedi and M. Badrkhani Asl, On special subalgebras of derivations of Lie algebras, Asian-Eur. J. Math. 8(2) (2015) 1550032] recently studied the central derivation of nilpotent Lie algebra with nilindex 2. The purpose of the present paper is to continue and extend the investigation to obtain some similar results for Lie superalgebras, as isoclinism in Lie superalgebra is being recently introduced.

Nilpotent fuzzy lie ideals

2020 ◽  
Vol 39 (3) ◽  
pp. 4071-4079
Author(s):  
E. Mohammadzadeh ◽  
G. Muhiuddin ◽  
J. Zhan ◽  
R.A. Borzooei
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Lie Ideal ◽  
Nilpotent Lie Algebra

In this paper, we introduce a new definition for nilpotent fuzzy Lie ideal, which is a well-defined extension of nilpotent Lie ideal in Lie algebras, and we name it a good nilpotent fuzzy Lie ideal. Then we prove that a Lie algebra is nilpotent if and only if any fuzzy Lie ideal of it, is a good nilpotent fuzzy Lie ideal. In particular, we construct a nilpotent Lie algebra via a good nilpotent fuzzy Lie ideal. Also, we prove that with some conditions, every good nilpotent fuzzy Lie ideal is finite. Finally, we define an Engel fuzzy Lie ideal, and we show that every Engel fuzzy Lie ideal of a finite Lie algebra is a good nilpotent fuzzy Lie ideal. We think that these notions could be useful to solve some problems of Lie algebras with nilpotent fuzzy Lie ideals.

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