Nekomutativní geometrie kvantových vlajkových variet
| Thesis title in Czech: | Nekomutativní geometrie kvantových vlajkových variet |
|---|---|
| Thesis title in English: | Noncommutative geometry of quantum flag manifolds |
| Key words: | kvantová grupa|nekomutativní geometrie|teorie reprezentace|sekvence Atiyah|Konexe |
| English key words: | quantum group|noncommutative geometry|representation theory|the Atiyah sequence|connections |
| Academic year of topic announcement: | 2024/2025 |
| Thesis type: | dissertation |
| Thesis language: | čeština |
| Department: | Mathematical Institute of Charles University (32-MUUK) |
| Supervisor: | Dr. Re O'Buachalla, Dr. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 29.09.2024 |
| Date of assignment: | 29.09.2024 |
| Confirmed by Study dept. on: | 29.09.2024 |
| Guidelines |
| The thesis aims to examine the noncommutative differential geometry of the D-series quantum flag manifolds. This will be done using a wide variety of tools, and a number of complementary points of view. For example, from algebra side it will use the theory of Hopf-Galois extensions, noncommutative differential calculi, quantum principal bundles, bimodule connections, the representation theory of the Drinfeld-Jimbo quantum groups, Lusztig's quantum root vectors, and quantum Schubert cells. Moreover, from the analytic side it will use C*-algebras, K-theory, and Connes' theory of spectral triples. |
| References |
| E. Beggs and S. Majid, Quantum Riemannian geometry, 1 ed., Grundlehren der mathematischen Wissenschaften, vol. 355, Springer International Publishing, 2019.
D. Huybrechts, Complex geometry: an introduction, 1 ed., Universitext, Springer– Verlag Berlin Heidelberg, 2005. I. Heckenberger and S. Kolb, The locally finite part of the dual coalgebra of quantized irreducible flag manifolds, Proc. London Math. Soc. (3) 89 (2004), no. 2, 457–484 I. Heckenberger and S. Kolb, De Rham complex for quantized irreducible flag mani- folds, J. Algebra 305 (2006), no. 2, 704–741 I. Heckenberger and S. Kolb, Differential forms via the Bernstein-Gelfand-Gelfand resolution for quantized irreducible flag manifolds, J. Geom. Phys. 57 (2007), no. 11, 2316–2344. R. O ́ Buachalla, Noncommutative complex structures on quantum homogeneous spaces, J. Geom. Phys. 99 (2016), 154–173 R. O ́ Buachalla, Noncommutative K ̈ahler structures on quantum homogeneous spaces, Adv. Math. 322 (2017), 892–939 |