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Izv. RAN. Ser. Mat., 2004, Volume 68, Issue 1, Pages 183–206 (Mi izv470)  

This article is cited in 10 scientific papers (total in 10 papers)

Prime alternative algebras that are nearly commutative

S. V. Pchelintsev


Abstract: We prove that by deforming the multiplication in a prime commutative alternative algebra using a C-operation we obtain a prime non-commutative alternative algebra. Under certain restrictions on non-commutative algebras this relation between algebras is reversible. Isotopes are special cases of deformations. We introduce and study a linear space generated by the Bruck C-operations. We prove that the Bruck space is generated by operations of rank 1 and 2 and that “general” Bruck operations of rank 2 are independent in the following sense: a sum of $n$ operations of rank 2 cannot be written as a linear combination of $(n-1)$ operations of rank 2 and an arbitrary operation of rank 1. We describe infinite series of non-isomorphic prime non-commutative algebras of bounded degree that are deformations of a concrete prime commutative algebra.

DOI: https://doi.org/10.4213/im470

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English version:
Izvestiya: Mathematics, 2004, 68:1, 181–204

Bibliographic databases:

UDC: 512.554.5
MSC: 17D05
Received: 03.12.2002

Citation: S. V. Pchelintsev, “Prime alternative algebras that are nearly commutative”, Izv. RAN. Ser. Mat., 68:1 (2004), 183–206; Izv. Math., 68:1 (2004), 181–204

Citation in format AMSBIB
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\pages 183--206
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\pages 181--204
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Pchelintsev, “Structure of finitely generated commutative alternative algebras and special Moufang loops”, Math. Notes, 80:3 (2006), 396–402  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. S. V. Pchelintsev, “Exceptional prime alternative algebras”, Siberian Math. J., 48:6 (2007), 1060–1073  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    3. S. V. Pchelintsev, “Degenerate alternative algebras”, Siberian Math. J., 55:2 (2014), 323–335  mathnet  crossref  mathscinet  isi
    4. A. S. Panasenko, “Just Infinite Alternative Algebras”, Math. Notes, 98:5 (2015), 805–812  mathnet  crossref  crossref  mathscinet  isi  elib
    5. S. V. Pchelintsev, “Isotopes of the alternative monster and the Skosyrsky algebra”, Siberian Math. J., 57:4 (2016), 666–678  mathnet  crossref  crossref  isi  elib  elib
    6. V. N. Zhelyabin, A. S. Panasenko, “Nil Ideals of Finite Codimension in Alternative Noetherian Algebras”, Math. Notes, 101:3 (2017), 460–466  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Pchelintsev S.V., “Proper identities of finitely generated commutative alternative algebras”, J. Algebra, 470 (2017), 425–440  crossref  mathscinet  zmath  isi  elib  scopus
    8. S. V. Pchelintsev, O. V. Shashkov, “Simple $5$-dimensional right alternative superalgebras with trivial even part”, Siberian Math. J., 58:6 (2017), 1078–1089  mathnet  crossref  crossref  isi  elib
    9. S. V. Pchelintsev, “Prime algebras connected with monsters”, Siberian Math. J., 59:2 (2018), 341–356  mathnet  crossref  crossref  isi  elib
    10. V. N. Zhelyabin, A. S. Panasenko, “Nearly finite-dimensional Jordan algebras”, Algebra and Logic, 57:5 (2018), 336–352  mathnet  crossref  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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