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Heisenberg groups over composition algebras

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Abstract

We solve the isomorphism problem for Heisenberg groups constructed over composition algebras, including the split case and characteristic two. We prove that two such groups are isomorphic if, and only if, the corresponding composition algebras are isomorphic as \(\mathbb Z\)-algebras.

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Notes

  1. Our notation follows Knarr and Stroppel (2015) and thus Dembowski (1968, 3.1.32) [cf. also Knarr and Stroppel (2013)], where geometrical aspects lead to an assignment of roles for the three bijections that may appear confusing to a reader of a more algebraic bent.

  2. Note that \({\text {Atp}}(A)\le \Psi _{A}\) in this case.

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Authors and Affiliations

  1. LExMath, Fakultät für Mathematik und Physik, Universität Stuttgart, 70550, Stuttgart, Germany

    Norbert Knarr & Markus Johannes Stroppel

Authors
  1. Norbert Knarr
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  2. Markus Johannes Stroppel
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Correspondence to Markus Johannes Stroppel.

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Knarr, N., Stroppel, M.J. Heisenberg groups over composition algebras. Beitr Algebra Geom 57, 667–677 (2016). https://doi.org/10.1007/s13366-015-0276-0

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  • DOI: https://doi.org/10.1007/s13366-015-0276-0

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