Skip to main content
SpringerLink
Log in

Simple Asymmetric Doubles, Their Automorphisms and Derivations

  • Published:
Algebra and Logic Aims and scope

A simple right-alternative, but not alternative, superalgebra whose even part coincides with an algebra of second-order matrices is called an asymmetric double. It is known that such superalgebras are eight-dimensional. We give a solution to the isomorphism problem for asymmetric doubles, point out their automorphism groups and derivation superalgebras.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. N. Jacobson, Lie Algebras, Wiley, New York (1962).

    MATH  Google Scholar 

  2. R. D. Schafer, An Introduction to Nonassociative Algebras, Pure Appl. Math., 22, Academic Press, London (1966).

  3. J. Tits, “Algèbres alternatives, algèbres de Jordan et algèbres de Lie exceptionnelles. I: Construction,” Nederl. Akad. Wet., Proc., Ser. A, 69, 223-237 (1966).

    Article  Google Scholar 

  4. S. V. Pchelintsev and O. V. Shashkov, “Simple finite-dimensional right-alternative superalgebras of Abelian type of characteristic zero,” Izv. Ross. Akad. Nauk, Mat., 79, No. 3, 131-158 (2015).

    Article  MathSciNet  Google Scholar 

  5. J. P. da Silva, L. S. I. Murakami, and I. Shestakov, “On right alternative superalgebras,” Comm. Alg., 44, No. 1, 240-252 (2016).

  6. S. V. Pchelintsev and O. V. Shashkov, “Simple right-alternative unital superalgebras over an algebra of matrices of order 2,” Algebra and Logic, 58, No. 1, 77-94 (2019).

    Article  MathSciNet  Google Scholar 

  7. S. V. Pchelintsev and O. V. Shashkov, “Simple asymmetric doubles, their automorphisms and derivations,” Mal’tsev Readings (2018), p. 165.

  8. A. A. Albert, “On right alternative algebras,” Ann. Math. (2), 50, 318-328 (1949).

    Article  MathSciNet  Google Scholar 

  9. A. I. Mal’tsev, Fundamentals of Linear Algebra [in Russian], Lan’, St. Petersburg (2009).

  10. I. N. Herstein, Noncommutative Rings, The Carus Math. Monogr., 15, Math. Ass. Am. (1968).

  11. F. R. Gantmakher, Matrix Theory [in Russian], Fizmatlit, Moscow (2010).

Download references

Author information

Authors and Affiliations

  1. Finance Academy under the Government of the Russian Federation, Leningradskii pr. 49, Moscow, 125993, Russia

    S. V. Pchelintsev & O. V. Shashkov

Authors
  1. S. V. Pchelintsev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. V. Shashkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. V. Pchelintsev.

Additional information

Translated from Algebra i Logika, Vol. 58, No. 5, pp. 627-649, September-October, 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pchelintsev, S.V., Shashkov, O.V. Simple Asymmetric Doubles, Their Automorphisms and Derivations. Algebra Logic 58, 417–433 (2019). https://doi.org/10.1007/s10469-019-09561-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10469-019-09561-z

Keywords

Search

Navigation