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Classification of 8-dimensional real two-step nilpotent Lie algebras

Published on:

22 August 2023

Primary Category:

Group Theory

Paper Authors:

Mikhail Borovoi,

Bogdan Adrian Dina,

Willem A. de Graaf


Key Details

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

AI generated summary

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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