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Vortrag - Rinat Kashaev (University of Geneva)

Quantised dihedral angles and quantum dilogarithms
Wann 11.06.2018
von 13:15 bis 14:15
Wo FRIAS, Albertstr. 19, Hörsaal
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I will describe a relation between quantum dilogarithms and 3-dimensional hyperbolic geometry obtained by quantising the dihedral angles of an ideal hyperbolic tetrahedron with respect to the Neumann-Zagier symplectic structure. In this way, one constructs a
(metaplectic) quantum operator $Q$ realising the 3-3 Pachner move for 4-dimensional triangulations. This realisation admits a natural generalisation to any self-dual locally compact abelian group, together with a fixed gaussian exponential. The 5-term operator identity, satisfied by a quantum dilogarithm over such a group, is equivalent to an integral identity involving the operator kernel of $Q$.