V. N. Zhelyabin, A. A. Popov, I. P. Shestakov, “The coordinate ring of an <nobr>$n$</nobr>-dimensional sphere and some examples of differentially simple algebras”, Algebra Logika, 2013, Volume 52, Number 4,Pages <nobr>416

This article is cited in 3 papers

The coordinate ring of an $n$-dimensional sphere and some examples of differentially simple algebras

V. N. Zhelyabin^ab, A. A. Popov^ab, I. P. Shestakov^ca

^a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
^b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
^c Universidade de São Paulo, Instituto de Matemática e Estatística, São Paulo-SEP, 05315-970, Brasil

Abstract: Using the coordinate ring of an $n$-dimensional real sphere, we construct examples of differentially simple algebras which are finitely generated projective, but nonfree, modules over their centroids. As a consequence, examples of such algebras are obtained in varieties of associative, Lie, alternative, Mal'tsev, and Jordan algebras.

Keywords: differentially simple algebra, module, centroid, variety, Lie algebra, alternative algebra, Mal’tsev algebra, Jordan algebra.

UDC: 512.554

Received: 26.12.2012
Revised: 16.07.2013