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Division algebras of degree 4 and 8 with involution

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Abstract

We develop necessary and sufficient conditions for central simple algebras to have involutions of the first kind, and to be tensor products of quaternion subalgebras. The theory is then applied to give an example of a division algebra of degree 8 with involution (of the first kind), without quaternion subalgebras, answering an old question of Albert; another example is a division algebra of degree 4 with involution (*) has no (*)-invariant quaternion subalgebras.

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References

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Authors and Affiliations

  1. Hebrew University of Jerusalem, Jerusalem, Israel

    S. A. Amitsur, L. H. Rowen & J. P. Tignol

  2. Institute for Advanced Studies, Mount Scopus, Jerusalem, Israel

    S. A. Amitsur, L. H. Rowen & J. P. Tignol

  3. Universite Catholique de Louvain, Louvain-la-Neuve, Belgium

    S. A. Amitsur, L. H. Rowen & J. P. Tignol

Authors
  1. S. A. Amitsur
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  2. L. H. Rowen
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  3. J. P. Tignol
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Additional information

The research of the second author is supported by the Anshel Pfeffer Chair.

The third author would like to express his gratitude to Professor J. Tits for many stimulating conversations.

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Amitsur, S.A., Rowen, L.H. & Tignol, J.P. Division algebras of degree 4 and 8 with involution. Israel J. Math. 33, 133–148 (1979). https://doi.org/10.1007/BF02760554

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  • DOI: https://doi.org/10.1007/BF02760554

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