Quantum algebras and Lie groups
Enrico Celeghini
Abstract
Lie groups and quantum algebras are connected through their common universal enveloping algebra. The adjoint action of Lie group on its algebra is naturally extended to related q-algebra and q-coalgebra. In such a way, quantum structure can be dealt more or less as the Lie one and we do not need to introduce the not easy to handle topological groups. Composed system also is described by the suitably symmetrized q-coalgebra. A physical application to the phonon, irreducible unitary representation of Eq(1,1), shows both the transformation under the group action of one phonon state and the fusion of two phonons, by means of the coproduct, in only one phonon lying on a branch of the appropriate dispersion relation.
Create a lesson
Related papers
Conformal field theory from automorphic forms on a quantum group
Dalimil Mazac
Anomaly effective actions for 4d N=1 superconformal field theories
Pantelis Panopoulos, Ioannis Papadimitriou
Exact Splitting of Amplitudes and One-Loop Integrands: A Classical Origin of Zeros
Yang Li, Laurentiu Rodina, Zhi-Zhen Wang
5-brane webs and generalised symmetries
Mohammad Akhond, Federico Carta, Sung-Soo Kim et al.
Form Factors in AdS from the Worldsheet
Luis F. Alday, Clément Virally, Xinan Zhou
Higher Integrability, Generalized Symmetries, and Partially Topological Field Theories
Luigi Alfonsi, Leron Borsten, Mehran Jalali Farahani et al.