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

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Algebra and Logic Aims and scope

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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    V. N. Zhelyabin & A. A. Popov

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    V. N. Zhelyabin

  3. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    A. A. Popov

  4. Universidade de São Paulo, São Paulo-SEP, 05315-970, Brasil

    I. P. Shestakov

  5. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    I. P. Shestakov

Authors
  1. V. N. Zhelyabin
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  2. A. A. Popov
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  3. I. P. Shestakov
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Correspondence to V. N. Zhelyabin.

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*Supported by RFBR (project No. 11-01-00938-a), by FAPESP (grant No. 2010/50347-9), and by CNPq (grant No. 305344/2009-9).

Translated from Algebra i Logika, Vol. 52, No. 4, pp. 416-434, July-August, 2013.

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Zhelyabin, V.N., Popov, A.A. & Shestakov, I.P. The coordinate ring of an n-dimensional sphere and some examples of differentially simple algebras. Algebra Logic 52, 277–289 (2013). https://doi.org/10.1007/s10469-013-9242-9

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  • DOI: https://doi.org/10.1007/s10469-013-9242-9

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