摘要: We give an elementary introduction to the theory of algebraic and topological quantum groups (in spirit S. L. Woronowicz). In particular, we recall basic facts from Hopf (*-) algebra theory, compact (matrix) their actions on spaces. also provide most important examples, including classification SL(2)-groups, real forms spheres. consider SLq(N)-groups Lorentz groups.
harvard.edu
sci-hub.se 参考文章(25)
Marc Rosso, Algèbres enveloppantes quantifiées, groupes quantiques compacts de matrices et calcul différentiel non commutatif Duke Mathematical Journal. ,vol. 61, pp. 11- 40 ,(1990) , 10.1215/S0012-7094-90-06102-2
S. L. Woronowicz, Unbounded elements affiliated withC*-algebras and non-compact quantum groups Communications in Mathematical Physics. ,vol. 136, pp. 399- 432 ,(1991) , 10.1007/BF02100032
Piotr Kondratowicz, Piotr Podleś, On representation theory of quantum $SL_{q}(2)$ groups at roots of unity Banach Center Publications. ,vol. 40, pp. 223- 248 ,(1997) , 10.4064/-40-1-223-248
Brian Parshall, Jian Pan Wang, Quantum linear groups ,(1991)
S. L. Woronowicz, S. Zakrzewski, Quantum Lorentz Group Having Gauss Decomposition Property Publications of The Research Institute for Mathematical Sciences. ,vol. 28, pp. 809- 824 ,(1992) , 10.2977/PRIMS/1195167937
Mitsuhiro Takeuchi, Quantum orthogonal and symplectic groups and their embedding into quantum $GL$ Proceedings of the Japan Academy, Series A, Mathematical Sciences. ,vol. 65, pp. 55- 58 ,(1989) , 10.3792/PJAA.65.55
Joachim Apel, Konrad Schm�dgen, Classification of three-dimensional covariant differential calculi on Podles' quantum spheres and on related spaces Letters in Mathematical Physics. ,vol. 32, pp. 25- 36 ,(1994) , 10.1007/BF00761121
S.L. Woronowicz, New quantum deformation of SL(2,C). Hopf algebra level Reports on Mathematical Physics. ,vol. 30, pp. 259- 269 ,(1991) , 10.1016/0034-4877(91)90030-Q
Takahiro Hayashi, Quantum deformation of classical groups Publications of The Research Institute for Mathematical Sciences. ,vol. 28, pp. 57- 81 ,(1992) , 10.2977/PRIMS/1195168856
S. L. Woronowicz, Compact matrix pseudogroups Communications in Mathematical Physics. ,vol. 111, pp. 613- 665 ,(1987) , 10.1007/BF01219077