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March 29, 2026Open Access

Classification of Finite Dimensional Nilpotent Lie Superalgebras by their Multipliers

SNS. NayakInstitute of Physics, Bhubaneshwar

Key Points

This research aims to classify finite dimensional nilpotent Lie superalgebras with specific Schur multipliers.
Examined nilpotent Lie superalgebras of dimension (m | n)
Investigated cases where the Schur multiplier s(L) equals 2
Listed non-abelian nilpotent Lie superalgebras with t(L) equal to 4.
Identified all nilpotent Lie superalgebras L with s(L) = 2.
Compiled a complete list of non-abelian nilpotent Lie superalgebras with t(L) = 4.

Abstract

Let L be a nilpotent Lie superalgebra of dimension (m | n) and, where M(L) denotes the Schur multiplier of L .Here s(L) 0 and the structure of all nonabelian nilpotent Lie superalgebras with s(L) = 0 is known 23.This paper is devoted to obtain all nilpotent Lie superalgebras L when s(L) 2. Further, we apply those results to list all non-abelian nilpotent Lie superalgebras L with t(L) 4 .

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