(Lie) Groups are typically seen as encoding a symmetry structure. For some phase spaces, the symmetry structure might need to be equipped with a non-trivial Poisson structure, which must then be compatible with the group product (to have a well defined symmetry action). This defines the notion of Poisson Lie group. When quantizing the system, the Poisson Lie group becomes a quantum group. I will provide a compact introduction to these concepts having in mind as leading example, the 3d (quantum) gravity framework, where such Poisson Lie/quantum symmetries are key to understand the quantum theory.
By Jan Ambjorn
By Jan Ambjorn
By Jan Ambjorn
By Jan Ambjorn
By Robert de Mello Koch
By Robert de Mello Koch
By Sanjaye Ramgoolam
By Sanjaye Ramgoolam
By Sanjaye Ramgoolam
By Sanjaye Ramgoolam
By Razvan Gurau
By Razvan Gurau
By Razvan Gurau
By Razvan Gurau
By François David
By Albert Schwarz
By Claudio Dappiaggi
By Alexander Strohmaier
By Ronnie Pavlov
By Tamara Kucherenko
