Special Issue "Quantum Group Symmetry and Quantum Geometry"
Deadline for manuscript submissions: 31 May 2021.
Interests: mathematical physics; classical and quantum integrable systems; quantum groups; noncommutative geometry; quantum gravity
Interests: quantum gravity phenomenology; deformed relativistic symmetries; primordial cosmology; quantum groups; noncommutative geometry
Quantum groups appeared during the eighties as the underlying algebraic symmetries of several two-dimensional integrable models. They are noncommutative generalizations of Lie groups endowed with a Hopf algebra structure, and the possibility of defining noncommutative spaces that are covariant under quantum group (co)actions soon provided a fruitful link with noncommutative geometry. At the same time, when quantum group analogues of the Lie groups of spacetime symmetries (Galilei, Poincaré and (anti-) de Sitter) were constructed, they attracted the attention of quantum gravity researchers. In fact, they provided a possible mathematical framework to model the "quantum" geometry of space–time and the quantum deformations of its kinematical symmetries at the Planck scale, where nontrivial features are expected to arise because of the interplay between gravity and quantum theory.
This Special Issue is open to contributions dealing with any of the many facets of quantum group symmetry and their generalizations. On the more formal side, possible topics include the theory of Poisson–Lie groups and Poisson homogeneous spaces as the associated semiclassical objects; Hopf algebras; the classification of quantum groups and spaces, their representation theory and its connections with q-special functions; the construction of noncommutative differential calculi; and the theory of quantum bundles. On application side, possible topics are: classical and quantum integrable models with quantum group invariance; the applications of quantum groups in different (2+1) quantum gravity contexts (like combinatorial quantisation, state sum models or spin foams); and quantum kinematical groups and their noncommutative spacetimes in connection with deformed special relativity and quantum gravity phenomenology.
Prof. Dr. Ángel Ballesteros
Dr. Giulia Gubitosi
Prof. Dr. Francisco J. Herranz
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
- quantum groups
- Poisson–Lie groups
- Lie bialgebras and r-matrices
- Poisson homogeneous spaces
- non-commutative differential calculi
- integrable models
- quantum gravity
- deformed symmetries
- noncommutative spacetimes