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SO(3)-Irreducible Geometry in Complex Dimension Five and Ternary Generalization of Pauli Exclusion Principle
Version 1
: Received: 6 November 2023 / Approved: 6 November 2023 / Online: 7 November 2023 (02:50:08 CET)
A peer-reviewed article of this Preprint also exists.
Abramov, V.; Liivapuu, O. SO(3)-Irreducible Geometry in Complex Dimension Five and Ternary Generalization of Pauli Exclusion Principle. Universe 2024, 10, 2. Abramov, V.; Liivapuu, O. SO(3)-Irreducible Geometry in Complex Dimension Five and Ternary Generalization of Pauli Exclusion Principle. Universe 2024, 10, 2.
Abstract
We propose a notion of a ternary skew-symmetric covariant tensor of 3rd order, consider it as a 3-dimensional matrix and study a ten-dimensional complex space of these tensors. We split this space into a direct sum of two five-dimensional subspaces and in each subspace there is an irreducible representation of the rotation group SO(3)↪SO(5). We find two independent SO(3)-invariants of ternary skew-symmetric tensors, where one of them is the Hermitian metric and the other is the quadratic form. We find the stabilizer of this quadratic form and its invariant properties. Making use of these invariant properties we define a SO(3)-irreducible geometric structure on a five-dimensional complex Hermitian manifold. We study a connection on a five-dimensional complex Hermitian manifold with a SO(3)-irreducible geometric structure, find its curvature and torsion. The structures proposed in this paper and their study are motivated by a ternary generalization of the Pauli’s principle proposed by R. Kerner.
Keywords
tensors; rotation group; tensor irreducible representations; complex manifolds; special geometries; connection; Pauli’s exclusion principle
Subject
Computer Science and Mathematics, Geometry and Topology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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