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
Proof of the AGT Conjecture at Generic β
Le-Feng Chen, Kilar Zhang
Casimir operators of 4D\,, N=2 supersymmetry in the harmonic approach
Egor Eremeev, Evgeny Ivanov
Doubly-scaled planar N = 4 SYM \& Carroll Holography
Arjun Bagchi, Prateksh Dhivakar, Alok Laddha et al.
Quantum Selection of Classical Histories
Omer Guleryuz
Wess-Zumino gauge for analytic prepotentials of off-shell N=2 supergravity: bosonic sector
Nikita Zaigraev, Julia Zernina
Testing holographic computation of entanglement pseudo-entropy in dS3/ICFT2
Liang Li