On the bicrossproduct structures for the family of algebras

Bueno, J. C. Pérez

doi:10.1088/0305-4470/31/30/015

J. Phys. A: Math. Gen.

1998

DOI: 10.1088/0305-4470/31/30/015

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On the bicrossproduct structures for the family of algebras

J. C. Pérez Bueno¹

Abstract: It is shown that the family of deformed algebras U λ (iso ω 2 ...ω N (N )) has a different bicrossproduct structure for each ω a = 0 in analogy to the undeformed case.

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Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra

Papageorgiou

Schroers

2010

J. High Energ. Phys.

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We define a theory of Galilean gravity in 2+1 dimensions with cosmological constant as a Chern-Simons gauge theory of the doubly-extended Newton-Hooke group, extending our previous study of classical and quantum gravity in 2+1 dimensions in the Galilean limit. We exhibit an r-matrix which is compatible with our Chern-Simons action (in a sense to be defined) and show that the associated bi-algebra structure of the Newton-Hooke Lie algebra is that of the classical double of the extended Heisenberg algebra. We deduce that, in the quantisation of the theory according to the combinatorial quantisation programme, much of the quantum theory is determined by the quantum double of the extended q-deformed Heisenberg algebra.

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Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra

Papageorgiou

Schroers

2010

J. High Energ. Phys.

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Projective representations ofk-Galilei group

Gonera

Kosiński

Maślanka

et al. 1998

J. Phys. A: Math. Gen.

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On the bicrossproduct structures for the family of algebras

Abstract: It is shown that the family of deformed algebras U λ (iso ω 2 ...ω N (N )) has a different bicrossproduct structure for each ω a = 0 in analogy to the undeformed case.

Cited by 2 publications

References 25 publications

Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra

Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra

Projective representations ofk-Galilei group

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