Multiplicative Lie algebras and Schur multiplier

In this paper, we give some equivalent conditions for Lie algebras to be isoclinic. In particular, it is shown that if two Lie algebras L and K are isoclinic then L can be constructed from K and vice versa using the operations of forming direct sums, taking subalgebras, and factoring Lie algebras. We also study connection between isoclinic and the Schur multiplier of Lie algebras. In addition, we deal with some properties of covers of Lie algebras whose Schur multipliers are finite dimensional and prove that all covers of any abelian Lie algebra have Hopfian property. Finally, we indicate that if a Lie algebra L belongs to some certain classes of Lie algebras then so does its cover.

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BOUNDS FOR THE DIMENSION OF THE SCHUR MULTIPLIER OF A PAIR OF NILPOTENT LIE ALGEBRAS

Asian-European Journal of Mathematics ◽

10.1142/s1793557112500593 ◽

2012 ◽

Vol 05 (04) ◽

pp. 1250059 ◽

Cited By ~ 1

Author(s):

Ali Reza Salemkar ◽

Somaieh Alizadeh Niri

Keyword(s):

Lie Algebras ◽

Schur Multiplier ◽

Nilpotent Lie Algebras ◽

Finite Dimensional ◽

Commutator Subalgebra

Let (L, N) be a pair of finite-dimensional nilpotent Lie algebras, in which N is an ideal in L. In this paper we derive some inequalities for the dimension of the Schur multiplier of the pair (L, N) in terms of the dimension of the commutator subalgebra [L, N].

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

Journal of Algebra and Its Applications ◽

10.1142/s0219498820500127 ◽

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.

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THE MULTIPLIER AND THE COVER OF DIRECT SUMS OF LIE ALGEBRAS

Asian-European Journal of Mathematics ◽

10.1142/s179355711250026x ◽

2012 ◽

Vol 05 (02) ◽

pp. 1250026 ◽

Cited By ~ 3

Author(s):

Ali Reza Salemkar ◽

Behrouz Edalatzadeh

Keyword(s):

Tensor Product ◽

Lie Algebras ◽

Schur Multiplier ◽

Direct Sums ◽

Schur Multipliers ◽

Direct Sum ◽

Group Case

In this paper, we prove that the Schur multiplier of the direct sum of two arbitrary Lie algebras is isomorphic to the direct sum of the Schur multipliers of the direct factors and the usual tensor product of the Lie algebras, which is similar to the work of Miller (1952) in the group case. Also, a cover for the direct sum of two Lie algebras in terms of given covers of them will be constructed.

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Capability and Schur multiplier of a pair of Lie algebras

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2016.11.016 ◽

2017 ◽

Vol 114 ◽

pp. 184-196 ◽

Cited By ~ 7

Author(s):

Farangis Johari ◽

Mohsen Parvizi ◽

Peyman Niroomand

Keyword(s):

Lie Algebras ◽

Schur Multiplier ◽

Pair Of Lie Algebras

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SOME PROPERTIES ON THE SCHUR MULTIPLIER OF A PAIR OF LIE ALGEBRAS

Journal of Algebra and Its Applications ◽

10.1142/s0219498811005348 ◽

2012 ◽

Vol 11 (01) ◽

pp. 1250011 ◽

Cited By ~ 4

Author(s):

MOHAMMAD REZA RISMANCHIAN ◽

MEHDI ARASKHAN

Keyword(s):

Lie Algebra ◽

Lie Algebras ◽

Central Extension ◽

Sufficient Condition ◽

Schur Multiplier ◽

Necessary And Sufficient Condition ◽

Pair Of Lie Algebras ◽

Necessary And Sufficient

The aim of this paper is to introduce the concept of the Schur multiplier [Formula: see text] of a pair of Lie algebras and to obtain some inequalities for the dimension of [Formula: see text]. Also, we consider some of the features of central extension of an arbitrary Lie algebra. Moreover, we present a necessary and sufficient condition in which the Schur multiplier of a pair of Lie algebras can be embedded into the Schur multiplier of their factor Lie algebras.

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