Addition to Block's theorem and to Popov's theorem on differentially simple algebras

V. N. Zhelyabin

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1375-1384

Résumé

The paper gives examples of differentially simple algebras over the field of complex numbers, which are not represented in the form specified in Block's theorem. More precisely, examples of these algebras are finitely generated projective, but non-free, modules over their centroids. Recall, Popov's theorem states, that a differentially simple alternative non-associative algebra over a field of characteristic zero is a finitely generated projective module over the center.

Détail

Keywords: differentially simple algebra, projective module, associative algebra, alternative algebra, Jordan algebra, Lie algebra, Malcev algebra algebra of polynomials.