论文标题
量子组和渐近对称性
Quantum Groups and Asymptotic Symmetries
论文作者
论文摘要
该论点致力于研究Bialgebra和Hopf代数结构，该结构与某些版本的非共同几何形状有关，这些几何形状是在无限二维的lie代数上构建的，这些代数是在Spacetime的渐近对称性的背景下出现的。我们证明了许多有关共同体学的定理，这些定理有助于分类双重分类，并明确构建和分析选定的HOPF代数。通过研究具有宇宙常数的空间的收缩极限，并将中央电荷纳入lie bialgebras和Hopf代数的水平，从而发现了特别有趣的行为。研究了现象学后果，例如从$κ$-Poincaré量子组的研究中知道的变形内部分散关系。此外，我们研究了在黑洞信息损失悖论和反对它的反复情况下，如何影响了一项新建议。
This thesis is devoted to the study of Lie bialgebra and Hopf algebra structures related to certain versions of non-commutative geometry constructed on infinite-dimensional 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 in-vacuo dispersion relations, known from the study of $κ$-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.
