Skip to main content
SpringerLink
Log in

Multipliers and weak multipliers of algebras

  • Original Paper
  • Published:
Acta Scientiarum Mathematicarum Aims and scope Submit manuscript

Abstract

We investigate general properties of multipliers and weak multipliers of algebras. We apply the results to determine the (weak) multipliers of associative algebras and zeropotent algebras of dimension 3 over an algebraically closed field.

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.

Institutional subscriptions

Similar content being viewed by others

Data availability

Not applicable.

Notes

  1. In general, for an associative algebra A over a field K of characteristic \(\ne 2\), the Jordan product \(\circ \) on A is defined by \(x\circ y = (xy + yx)/2\) for \(x, y \in A\).

  2. Usually \(A^2\) denotes the subspace of A generated by this subset.

  3. This is called a broadcasting (cf. [7]).

  4. This is the algebra taken up in [9].

References

  1. Johnson, B.E.: An introduction to the theory of centralizers. Proc. London Math. Soc. 14, 299–320 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  2. Kaniuth, E.: A Course in commutative Banach algebras. Springer, USA (2008)

    MATH  Google Scholar 

  3. Kobayashi, Y., Shirayanagi, K., Tsukada, M., Takahasi, S.-E.: A complete classification of three-dimensional algebras over \(\mathbb{R} \) and \(\mathbb{C} \), visiting old lean new. Asian-Eur. J. Math. 14, 2150131 (2021)

    Article  MATH  Google Scholar 

  4. Kobayashi, Y., Shirayanagi, K., Tsukada, M., Takahasi, S.-E.: Classification of three dimensional zeropotent algebras over an algebraically closed field. Commun. Algebra 45, 5037–5052 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  5. Larsen, R.: An introduction to the theory of multipliers. New York, Springer-Verlag, Berlin (1971)

    Book  MATH  Google Scholar 

  6. Laali, J., Fozouni, M.: \(n\)-multipliers and their relations with \(n\)-homomorphisms. Vietnam J. Math. 45, 451–457 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  7. Tsukada, M., et al.: Linear algebra with Python. Theory and Applications, Springer, USA

  8. Wendel, J.G.: Left Centralizers and Isomorphisms on group algebras. Pacific J. Math. 2, 251–261 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zivari-Kazempour, A.: Almost multipliers of Frechet algebras. J. Anal. 28(4), 1075–1084 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zivari-Kazempour, A.: Approximate \(\theta \)-multipliers on Banach algebras. Surv. Math. Appl. 77, 79–88 (2022)

    MathSciNet  MATH  Google Scholar 

  11. Zivari-Kazempour, A., Valaei, M.: pseudo-\(n\)-multiplier and Pseudo-\(n\)-Jordan multiplier. Analysis (2023). https://doi.org/10.1515/anly-2021-1009

Download references

Author information

Authors and Affiliations

  1. Laboratory of Mathematics and Games, Funabashi, Japan

    Yuji Kobayashi & Sin-Ei Takahasi

Authors
  1. Yuji Kobayashi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sin-Ei Takahasi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuji Kobayashi.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kobayashi, Y., Takahasi, SE. Multipliers and weak multipliers of algebras. Acta Sci. Math. (Szeged) (2023). https://doi.org/10.1007/s44146-023-00100-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s44146-023-00100-y

Keywords

Mathematics Subject Classification

Search

Navigation