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- Title
SO(3)-Irreducible Geometry in Complex Dimension Five and Ternary Generalization of Pauli Exclusion Principle.
- Authors
Abramov, Viktor; Liivapuu, Olga
- Abstract
Motivated by a ternary generalization of the Pauli exclusion principle proposed by R. Kerner, we propose a notion of a Z 3 -skew-symmetric covariant SO (3) -tensor of the third order, consider it as a 3-dimensional matrix, and study the geometry of the 10-dimensional complex space of these tensors. We split this 10-dimensional space into a direct sum of two 5-dimensional subspaces by means of a primitive third-order root of unity q, and in each subspace, there is an irreducible representation of the rotation group SO (3) ↪ SU (5) . We find two SO (3) -invariants of Z 3 -skew-symmetric tensors: one is the canonical Hermitian metric in five-dimensional complex vector space and the other is a quadratic form denoted by K (z , z) . We study the invariant properties of K (z , z) and find its stabilizer. Making use of these invariant properties, we define an SO (3) -irreducible geometric structure on a five-dimensional complex Hermitian manifold. We study a connection on a five-dimensional complex Hermitian manifold with an SO (3) -irreducible geometric structure and find its curvature and torsion.
- Subjects
COMPLEX manifolds; GEOMETRY; GENERALIZATION; VECTOR spaces; BIVECTORS; QUADRATIC forms; FINSLER spaces
- Publication
Universe (2218-1997), 2024, Vol 10, Issue 1, p2
- ISSN
2218-1997
- Publication type
Article
- DOI
10.3390/universe10010002