Quantum Groups and Asymptotic Symmetries
Abstract
This thesis is devoted to the study of Lie bialgebra and Hopf algebra structures related to certain versions of noncommutative geometry constructed on infinitedimensional Lie algebras that arise in the context of asymptotic symmetries of spacetime. We prove a number of theorems about cohomology groups that aid the classification of the Lie bialgebras and explicitly construct and analyze selected Hopf algebras. Particularly interesting behavior was found by studying the contraction limit of spacetimes with cosmological constant and the inclusion of central charges on the level of Lie bialgebras and Hopf algebras. Phenomenological consequences, like deformed invacuo dispersion relations, known from the study of $\kappa$Poincaré quantum groups, are investigated. Furthermore, we examine how a new proposal in the context of the black hole information loss paradox and counterarguments against it are affected.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.00453
 Bibcode:
 2022arXiv220500453U
 Keywords:

 Mathematical Physics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 PhD Thesis, 166 pages, 3 figures