• Title/Summary/Keyword: Quaternionic vector spac

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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
    • Journal of the Korean Mathematical Society
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    • v.61 no.3
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    • pp.547-564
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    • 2024
  • 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.