Structure and representations of finite dimensional Malcev algebras
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2023-02-15 17:09
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KUZMIN, Evghenii. Structure and representations of finite dimensional Malcev algebras. In: Quasigroups and Related Systems, 2014, vol. 22, nr. 1(31), pp. 97-132. ISSN 1561-2848.
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Quasigroups and Related Systems
Volumul 22, Numărul 1(31) / 2014 / ISSN 1561-2848

Structure and representations of finite dimensional Malcev algebras

Pag. 97-132

Kuzmin Evghenii
 
Sobolev Institute of Mathematics
 
Disponibil în IBN: 5 mai 2016


Rezumat

The paper [6] is devoted to the study of the basic structure theory of finite dimensional Malcev algebras. Similarly to the structure of finite dimensional Lie algebras, this theory has attracted a lot of attention and stimulated further research in this area. However, for the sake of brevity, detailed proofs of some results were omitted. Some authors experienced some dificulty owing to the lack of detailed proofs (see, for example [14]). The present work mostly follows the outline of [6] and fills the gaps in the literature.

Cuvinte-cheie
Malcev algebras, Cartan subalgebras, nilpotent algebras, representation theory, solvable algebras, semisimple algebras, classification of simple algebras in characteristic 0, conjugacy theorem for Cartan subalgebras.