Isoclinic extensions of Lie algebras | Zendy

Hamid Mohammadzadeh | Zendy; Ali Reza Salemkar | Zendy; Zahra Riyahi | Zendy

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Isoclinic extensions of Lie algebras

Author(s) -

Hamid Mohammadzadeh,

Ali Reza Salemkar,

Zahra Riyahi

Publication year - 2013

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1204-7

Subject(s) - mathematics , killing form , pure mathematics , schur multiplier , isomorphism (crystallography) , lie algebra , representation of a lie group , non associative algebra , algebra over a field , extension (predicate logic) , adjoint representation of a lie algebra , lie conformal algebra , computer science , symmetric group , alternating group , crystal structure , chemistry , programming language , crystallography

In this article we introduce the notion of the equivalence relation, isoclinism, on the central extensions of Lie algebras, and determine all central extensions occurring in an isoclinism class of a given central extension. We also show that under some conditions, the concepts of isoclinism and isomorphism between the central extensions of finite dimensional Lie algebras are identical. Finally, the connection between isoclinic extensions and the Schur multiplier of Lie algebras are discussed.

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