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Projective group representations in quaternionic Hilbert space [PDF]
Journal of Mathematical Physics, 1996 We extend the discussion of projective group representations in quaternionic Hilbert space that was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary operators and then analyzed in terms of their generator structure.
Emch G., Stephen L. Adler, Uhlhorn U.
openaire +6 more sources
Response to the Comment by G. Emch on Projective Group Representations in Quaternionic Hilbert Space [PDF]
J.Math.Phys. 37 (1996) 6586-6589, 1996 We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective
Adler, S. L.
arxiv +5 more sources
International Journal of Mathematics and Mathematical Sciences, 2013 The purpose of this paper is to study n-dimensional QR-submanifolds of (p−1)QR-dimension in a quaternionic projective space QP(n+p)/4 and especially to determine such submanifolds under some curvature conditions.
Hyang Sook Kim, Jin Suk Pak
doaj +2 more sources
On quaternionic bisectional curvature [PDF]
arXiv, 2023 In this article we study the concept of quaternionic bisectional curvature introduced by B. Chow and D. Yang for quaternion-K\"ahler manifolds. We show that non-negative quaternionic bisectional curvature is only realized for the quaternionic projective space. We also show that all symmetric quaternion-K\"ahler manifolds different from the quaternionic
Macia, Oscar +2 more
arxiv +2 more sources
Torus Action on Quaternionic Projective Plane and Related Spaces [PDF]
Arnold Mathematical Journal, 2020 22 pages, 6 ...
Ayzenberg, Anton
openaire +4 more sources
Involutions fixing HP1(2m)∪HP2(2m)∪HP(2n+1) of the fixed point set
Journal of Hebei University of Science and Technology, 2015 Let (Mr,T) be a smooth closed manifold of dimension r with a smooth involution T whose fixed point set is F=HP1(2m)∪HP2(2m)∪HP(2n+1)(m≥1), where HP(n) denotes the n-dimensional quaternionic projective space.
Suqian ZHAO
doaj +1 more source
On real hypersurfaces in quaternionic projective space with 𝒟⊥-recurrent second fundamental tensor
International Journal of Mathematics and Mathematical Sciences, 1999 In this paper, we give a complete classification of real hypersurfaces in a quaternionic projective space QPm with 𝒟⊥-recurrent second fundamental tensor under certain condition on the orthogonal distribution 𝒟.
Young Jin Suh, Juan De Dios Pérez
doaj +1 more source
Twistorial maps between quaternionic manifolds [PDF]
, 2008 We introduce a natural notion of quaternionic map between almost quaternionic manifolds and we prove the following, for maps of rank at least one: 1) A map between quaternionic manifolds endowed with the integrable almost twistorial structures is twistorial if and only if it is quaternionic.
arxiv +1 more source
Integrability of quaternion-Kähler symmetric spaces [PDF]
arXiv, 2020 We find a necessary condition for the existence of an action of a Lie group $G$ by quaternionic automorphisms on an integrable quaternionic manifold in terms of representations of $\mathfrak{g}$. We check this condition and prove that a Riemannian symmetric space of dimension $4n$ for $n\geq 2$ has an invariant integrable almost quaternionic structure ...
arxiv
Simple closed curves, non‐kernel homology and Magnus embedding
Journal of Topology, Volume 18, Issue 2, June 2025.Abstract We consider the subspace of the homology of a covering space spanned by lifts of simple closed curves. Our main result is the existence of unbranched covers of surfaces where this is a proper subspace. More generally, for a fixed finite solvable quotient of the fundamental group we exhibit a cover whose homology is not generated by the lifts ...
Adam Klukowski
wiley +1 more source