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Non-Alternating Hamiltonian Lie Algebras of Characteristic Two in Three Variables

Authors
  • Kondrateva, A. V.1
  • 1 National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, 603950, Russia , Nizhny Novgorod (Russia)
Type
Published Article
Journal
Lobachevskii Journal of Mathematics
Publisher
Pleiades Publishing
Publication Date
Dec 13, 2021
Volume
42
Issue
12
Pages
2841–2853
Identifiers
DOI: 10.1134/S1995080221120209
Source
Springer Nature
Keywords
Disciplines
  • Article
License
Yellow

Abstract

AbstractNon-alternating Hamiltonian Lie algebras in three variables over a perfect field of characteristic 2 are considered. A classification of non-alternating Hamiltonian forms over an algebra of divided powers in three variables and of the corresponding simple Lie algebras is given. In particular, it is shown that the non-alternating Hamiltonian form may not be equivalent to its linear part. It is proved that the Lie algebras which correspond to the nonequivalent forms are not isomorphic.

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