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Associative and Jordan Algebras Generated by Two Idempotents

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Abstract

The purpose of this note is to obtain precise information about associative or Jordan algebras generated by two idempotents.

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References

  1. Bergman, G.: Modules over coproducts of rings. Trans. Am. Math. Soc. 200, 1–32 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  2. De Medts, T., Rehren, F.: Jordan Algebras and 3-transposition groups. J. Algebra 478, 318–340 (2017)

  3. Hall, J.I., Rehren, F., Shpectorov, S.: Universal axial algebras and a theorem of Sakuma. J. Algebra 421, 394–424 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hall, J.I., Rehren, F., Shpectorov, S.: Primitive axial algebras of Jordan type. J. Algebra 437, 79–115 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hall, J.I., Segev, Y., Shpectorov, S.: Miyamoto involutions and axial algebras of Jordan type half. Israel J. Math., to appear, arXiv:1610.01307

  6. Herstein, I.N.: Noncommutative Rings. The Carus Mathematical Monographs, vol. 15. Published by The Mathematical Association of America; distributed by Wiley, New York (1968)

  7. Ivanov, A.A.: The monster group and majorana involutions. Cambridge Tracts in Mathematics 176 (2009)

  8. Jacobson, N.: Structure and Representations of Jordan Algebras. American Mathematical Society Colloquium Publications, vol. XXXIX. American Mathematical Society, Providence, R.I (1968)

  9. Jain, S.K.: Prime rings having one-sided ideal with polynomial identity coincide with special Johnson rings. J. Algebra 19, 125–130 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  10. Laffey, T.J.: Algebras generated by two idempotents. Linear Algebra Appl. 37, 45–53 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  11. Matsuo, A.: 3-transposition groups of symplectic type and vertex operator algebras. J. Math. Soc. Japan 57, 639–649 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Miyamoto, M.: Griess algebras and conformal vectors in vertex operator algebras. J. Algebra 179, 523–548 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  13. Rowen, L.H.: Graduate algebra: noncommutative view. AMS Graduate Studies in Mathematics 91 (2008)

  14. Sakuma, S.: 6-Transposition property of τ-involutions of vertex operator algebras. Int. Math. Res. Not. IMRN rnm030(9), 19 (2007)

    MathSciNet  MATH  Google Scholar 

  15. Vais, I.: Algebras that are Generated by Two Idempotents, (Russian) Seminar Analysis (Berlin, 1987/1988), 139–145. Akademie-Verlag, Berlin (1988)

  16. Zhevlakov, K.A., Slinko, A.M., Shestakov, I.P., Shirshov, A.I.: Rings that are Nearly Associative, Translated from the Russian by Harry F. Smith. Pure and Applied Mathematics, vol. 104, p. xi+371. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York–London (1982)

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Acknowledgments

We are grateful to the referee for a very careful reading of the manuscript, for spotting a gap (which was filled by means of Lemma 2.8), for the reformulation of Theorem 1.1(7) and for various remarks that improved our exposition.

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Authors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel

    Louis Rowen

  2. Department of Mathematics, Ben-Gurion University, Beer-Sheva, 84105, Israel

    Yoav Segev

Authors
  1. Louis Rowen
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  2. Yoav Segev
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Correspondence to Louis Rowen.

Additional information

Presented by Jon F. Carlson.

Louis Rowen partially supported by the Israel Science Foundation grant no. 1623/16.

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Rowen, L., Segev, Y. Associative and Jordan Algebras Generated by Two Idempotents. Algebr Represent Theor 20, 1495–1504 (2017). https://doi.org/10.1007/s10468-017-9697-9

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  • DOI: https://doi.org/10.1007/s10468-017-9697-9

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