Isoclinism in multiplicative Lie algebras
Mani Shankar Pandey, Sumit Kumar Upadhyay
TL;DR
This paper introduces the concepts of isoclinism and cover in multiplicative Lie algebras, providing conditions for the existence of stem multiplicative Lie algebras and their covers, aiding in classifying such structures.
Contribution
It defines isoclinism and covers in multiplicative Lie algebras and establishes criteria for the existence of stem covers, advancing the structural understanding of these algebras.
Findings
Existence of stem multiplicative Lie algebra proven
Necessary and sufficient conditions for stem cover established
Framework for classifying multiplicative Lie algebra structures developed
Abstract
The purpose of this paper is to introduce the notion of isoclinism and cover in a multiplicative Lie algebra which may be helpful to describe all multiplicative Lie algebra structures on a group. Consequently, we give the existence of the stem multiplicative Lie algebra. We also give the necessary and sufficient conditions for the existence of stem cover of a multiplicative Lie algebra.
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Taxonomy
TopicsAdvanced Topics in Algebra · Finite Group Theory Research · Algebraic structures and combinatorial models