Quaternionic and Poisson-Lie structures in 3d gravity: the cosmological constant as deformation parameter - General Relativity and Quantum CosmologyReportar como inadecuado




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Abstract: Each of the local isometry groups arising in 3d gravity can be viewed as thegroup of unit split quaternions over a ring which depends on the cosmologicalconstant. In this paper we explain and prove this statement, and use it as aunifying framework for studying Poisson structures associated with the localisometry groups. We show that, in all cases except for Euclidean signature withpositive cosmological constant, the local isometry groups are equipped with thePoisson-Lie structure of a classical double. We calculate the dressing actionof the factor groups on each other and find, amongst others, a simple andunified description of the symplectic leaves of SU2 and SL2,R. We alsocompute the Poisson structure on the dual Poisson-Lie groups of the localisometry groups and on their Heisenberg doubles; together, they determine thePoisson structure of the phase space of 3d gravity in the so-calledcombinatorial description.



Autor: Catherine Meusburger, Bernd Schroers

Fuente: https://arxiv.org/



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