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arXiv · 2509.03019

Correspondence, Wells and Hochschild-Serre sequences for nonabelian extensions of multiplicative Lie algebras

Alexander Wires·Dev Karan Singh·Shiv Datt Kumar
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Abstract

For nonabelian $2^{\mathrm{nd}}$-cohomology of multiplicative Lie algebras, we properly generalize from the group case three classic results. We prove a Correspondence theorem which compares $2^{\mathrm{nd}}$-cohomology associated to a realized abstract kernel to the abelian $2^{\mathrm{nd}}$-cohomology group over the algebraic center. For arbitrary extensions, we prove a Wells's Theorem characterizing ideal-preserving automorphisms and establish the 1-dimensional Lyndon-Hochschild-Serre exact sequence. Several previously established results are recovered when restricted to extensions with group-abelian or Lie-trivial ideals.

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Alexander Wires, Dev Karan Singh, Shiv Datt Kumar. 2025-09-03. Correspondence, Wells and Hochschild-Serre sequences for nonabelian extensions of multiplicative Lie algebras. https://arxiv.org/abs/2509.03019

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