| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 1851507 | Physics Letters B | 2016 | 6 Pages |
Abstract
We employ new calculational technique and present complete list of classical r -matrices for D=4D=4 complex homogeneous orthogonal Lie algebra o(4;C)o(4;C), the rotational symmetry of four-dimensional complex space–time. Further applying reality conditions we obtain the classical r -matrices for all possible real forms of o(4;C)o(4;C): Euclidean o(4)o(4), Lorentz o(3,1)o(3,1), Kleinian o(2,2)o(2,2) and quaternionic o⋆(4)o⋆(4) Lie algebras. For o(3,1)o(3,1) we get known four classical D=4D=4 Lorentz r-matrices, but for other real Lie algebras (Euclidean, Kleinian, quaternionic) we provide new results and mention some applications.
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Authors
A. Borowiec, J. Lukierski, V.N. Tolstoy,