SUBMAXIMALLY SYMMETRIC ALMOST QUATERNIONIC STRUCTURES
| Autor: | Lenka Zalabová, Boris Kruglikov, Henrik Winther |
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| Rok vydání: | 2017 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Algebra and Number Theory 010102 general mathematics Dimension (graph theory) Structure (category theory) VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Statistikk: 412 Curvature 01 natural sciences Differential Geometry (math.DG) 0103 physical sciences Homogeneous space FOS: Mathematics Mathematics::Differential Geometry 010307 mathematical physics Geometry and Topology 0101 mathematics Symmetry (geometry) Algebra over a field Quaternionic projective space Mathematics |
| Zdroj: | Transformation Groups. 23:723-741 |
| ISSN: | 1531-586X 1083-4362 |
| Popis: | This is a post-peer-review, pre-copyedit version of an article published in Transformation groups. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00031-017-9453-6. The symmetry dimension of a geometric structure is the dimension of its symmetry algebra. We investigate symmetries of almost quaternionic structures of quaternionic dimension n. The maximal possible symmetry is realized by the quaternionic projective space HP n, which is flat and has the symmetry algebra sl(n + 1, H) of dimension 4n 2 + 8n + 3. For non-flat almost quaternionic manifolds we compute the next biggest (submaximal) symmetry dimension. We show that it is equal to 4n 2−4n+9 for n > 1 (it is equal to 8 for n = 1). This is realized both by a quaternionic structure (torsion–free) and by an almost quaternionic structure with vanishing quaternionic Weyl curvature. |
| Databáze: | OpenAIRE |
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