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- W3100570959 abstract "It is shown that the canonical classical $r$-matrix arising from the Drinfel'd double structure underlying the two-fold centrally extended (2+1) Galilean and Newton-Hooke Lie algebras (with either zero or non-zero cosmological constant $Lambda$, respectively) originates as a well-defined non-relativistic contraction of a specific class of canonical $r$-matrices associated with the Drinfel'd double structure of the (2+1) (anti)-de Sitter Lie algebra. The full quantum group structure associated with such (2+1) Galilean and Newton-Hooke Drinfel'd doubles is presented, and the corresponding noncommutative spacetimes are shown to contain a commuting 'absolute time' coordinate ${hat x}_0$ together with two noncommutative space coordinates $({hat x}_1,{hat x}_2)$, whose commutator is a function of the cosmological constant $Lambda$ and of the (central) 'quantum time' coordinate ${hat x}_0$. Thus, the Chern-Simons approach to Galilean (2+1) gravity can be consistently understood as the appropriate non-relativistic limit of the Lorentzian theory, and their associated quantum group symmetries (which do not fall into the family of so-called kappa-deformations) can also be derived from the (anti)-de Sitter quantum doubles through a well-defined quantum group contraction procedure." @default.
- W3100570959 created "2020-11-23" @default.
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- W3100570959 date "2014-11-28" @default.
- W3100570959 modified "2023-10-03" @default.
- W3100570959 title "From Lorentzian to Galilean (2+1) gravity: Drinfelʼd doubles, quantization and noncommutative spacetimes" @default.
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- W3100570959 doi "https://doi.org/10.1088/0264-9381/31/24/245013" @default.
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