Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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TOTALLY REAL AND COMPLEX SUBSPACES OF A RIGHT QUATERNIONIC VECTOR SPACE WITH A HERMITIAN FORM OF SIGNATURE (n, 1)

  • Sungwoon Kim (Department of Mathematics Jeju National University)
  • Received : 2023.08.04
  • Accepted : 2024.02.16
  • Published : 2024.05.01
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Abstract

We study totally real and complex subsets of a right quarternionic vector space of dimension n + 1 with a Hermitian form of signature (n, 1) and extend these notions to right quaternionic projective space. Then we give a necessary and sufficient condition for a subset of a right quaternionic projective space to be totally real or complex in terms of the quaternionic Hermitian triple product. As an application, we show that the limit set of a non-elementary quaternionic Kleinian group 𝚪 is totally real (resp. commutative) with respect to the quaternionic Hermitian triple product if and only if 𝚪 leaves a real (resp. complex) hyperbolic subspace invariant.

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Acknowledgement

This research was supported by the 2023 Scientific Promotion Program funded by Jeju National University.

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