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Physical Sciences and Mathematics Commons™
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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
On Theta Pair For A Proper Subalgebra, Ali Reza Salemkar, Sara Chehrazi, Hamid Mohammadzadeh
On Theta Pair For A Proper Subalgebra, Ali Reza Salemkar, Sara Chehrazi, Hamid Mohammadzadeh
Turkish Journal of Mathematics
For a proper subalgebra K of a finite dimensional Lie algebra L, a pair (A,B) of subalgebras of L is called a \theta-pair if L = \langle A,K\rangle, B is the largest ideal of L contained in A\cap K and for each proper subalgebra C/B of A/B which is an ideal of L/B, we have L\neq C+K. In this article, using this concept, we give some characterizations of solvability and supersolvability of a finite dimensional Lie algebra.
Isoclinic Extensions Of Lie Algebras, Hamid Mohammadzadeh, Ali Reza Salemkar, Zahra Riyahi
Isoclinic Extensions Of Lie Algebras, Hamid Mohammadzadeh, Ali Reza Salemkar, Zahra Riyahi
Turkish Journal of Mathematics
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.
Cartan Equivalence Problem For Third-Order Differential Operators, Mehdi Nadjafikhah, Rohollah Bakhshandeh Chamazkoti
Cartan Equivalence Problem For Third-Order Differential Operators, Mehdi Nadjafikhah, Rohollah Bakhshandeh Chamazkoti
Turkish Journal of Mathematics
This article is dedicated to solving the equivalence problem for a pair of third-order differential operators on the line under general fiber-preserving transformation using the Cartan method of equivalence. We will treat 2 versions of equivalence problems: first, the direct equivalence problem, and second, an equivalence problem to determine conditions on 2 differential operators such that there exists a fiber-preserving transformation mapping one to the other according to gauge equivalence.