Published on:
22 August 2023
Primary Category:
Group Theory
Paper Authors:
Mikhail Borovoi,
Bogdan Adrian Dina,
Willem A. de Graaf
Uses known classification of 8D two-step nilpotent complex Lie algebras
Employs Galois cohomology to determine real forms
Reduces problem to orbit classification for classical groups
Computes component groups of stabilizers to apply Sansuc's lemma
Provides explicit structure constants for all 27 real isomorphism classes
Classification of 8-dimensional real two-step nilpotent Lie algebras
This paper classifies 8-dimensional real two-step nilpotent Lie algebras, which are Lie algebras where the commutator of any two elements lies in the center. The authors use known classification results over complex numbers, along with Galois cohomology, to explicitly determine the structure constants for all such real Lie algebras. They reduce the problem to classifying orbits of certain groups, then compute invariants of stabilizers to get the component groups needed for the cohomology computation.
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