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- W3125320432 abstract "Using the isomorphism $${mathfrak {o}}(3;{mathbb {C}})simeq {mathfrak {sl}}(2;{mathbb {C}})$$ we develop a new simple algebraic technique for complete classification of quantum deformations (the classical r-matrices) for real forms $${mathfrak {o}}(3)$$ and $${mathfrak {o}}(2,1)$$ of the complex Lie algebra $${mathfrak {o}}(3;{mathbb {C}})$$ in terms of real forms of $${mathfrak {sl}}(2;{mathbb {C}})$$ : $${mathfrak {su}}(2)$$ , $${mathfrak {su}}(1,1)$$ and $${mathfrak {sl}}(2;{mathbb {R}})$$ . We prove that the $$D=3$$ Lorentz symmetry $${mathfrak {o}}(2,1)simeq {mathfrak {su}}(1,1)simeq {mathfrak {sl}}(2;{mathbb {R}})$$ has three different Hopf-algebraic quantum deformations, which are expressed in the simplest way by two standard $${mathfrak {su}}(1,1)$$ and $${mathfrak {sl}}(2;{mathbb {R}})$$ q-analogs and by simple Jordanian $${mathfrak {sl}}(2;{mathbb {R}})$$ twist deformation. These quantizations are presented in terms of the quantum Cartan–Weyl generators for the quantized algebras $${mathfrak {su}}(1,1)$$ and $${mathfrak {sl}}(2;{mathbb {R}})$$ as well as in terms of quantum Cartesian generators for the quantized algebra $${mathfrak {o}}(2,1)$$ . Finally, some applications of the deformed $$D=3$$ Lorentz symmetry are mentioned." @default.
- W3125320432 created "2021-02-01" @default.
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- W3125320432 date "2017-04-01" @default.
- W3125320432 modified "2023-09-24" @default.
- W3125320432 title "Quantizations of $$D=3$$ D = 3 Lorentz symmetry" @default.
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- W3125320432 doi "https://doi.org/10.1140/epjc/s10052-017-4786-9" @default.
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