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The aim is to classify multiplicative Lie algebra structures on specific groups and determine their Schur multipliers.

March 29, 2026Journal of Lie theoryOpen Access

The Schur Multiplier of Some Finite Multiplicative Lie Algebras

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The aim is to classify multiplicative Lie algebra structures on specific groups and determine their Schur multipliers.
Classified multiplicative Lie algebra structures on symmetric and alternating groups.
Calculated the Schur multiplier and Lie exterior square for finite multiplicative Lie algebras.
Analyzed non abelian simple groups with trivial Schur multipliers.
Identified all multiplicative Lie algebra structures on symmetric and alternating groups.
Found that the Schur multiplier for non abelian simple groups is trivial if their Schur multiplier is trivial.
Showed that the Lie exterior square of non abelian groups is isomorphic to the group itself with an improper structure.

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Classification of multiplicative Lie algebra structures and Schur multipliers on group types, indicating structural properties.

Kumar et al. (2024) studied this question.

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