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Isotopism and isomorphism classes of certain Lie algebras over finite fields

 

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Opened Access Isotopism and isomorphism classes of certain Lie algebras over finite fields
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Author: Falcón Ganfornina, Óscar Jesús
Falcón Ganfornina, Raúl Manuel
Núñez Valdés, Juan
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Universidad de Sevilla. Departamento de Geometría y Topología
Date: 2015
Published in: Results in Mathematics, 1-17.
Document type: Article
Abstract: In the current paper, we study the distribution into isotopism and isomorphism classes of the relevant family FpnFnp of Lie algebras of basis {e1,…,en}{e1,…,en} and nonzero brackets [ei,en]∈⟨e1,…,en−1⟩[ei,en]∈⟨e1,…,en−1⟩ over a finite field FpFp , with p prime. At this end we first introduce the concept of the structure tuple of a Lie algebra and specifically prove that there exist n isotopism classes in FpnFnp and three families of isomorphism classes depending on the first component of their structure tuple.
Cite: Falcón Ganfornina, O.J., Falcón Ganfornina, R.M. y Núñez Valdés, J. (2016). Isotopism and isomorphism classes of certain Lie algebras over finite fields. Results in Mathematics, 1-17.
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URI: http://hdl.handle.net/11441/44770

DOI: 10.1007/s00025-015-0502-y

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