caa a22 4500 467954135 CHVBK 20180405193745.0 cr unu---uuuuu 170328e20041101xx s 000 0 eng 10.1007/s10440-005-4592-5 doi (NATIONALLICENCE)springer-10.1007/s10440-005-4592-5 (NATIONALLICENCE)springer-10.1007/s10440-004-5592-6 Cartan calculus for quantum differentials on bicrossproducts [Elektronische Daten] [F. Ngakeu, S. Majid, J. Ezin] We provide the Cartan calculus for bicovariant differential forms on bicrossproduct quantum groups k(M) k G associated to finite group factorizations X = GM and a field k. The irreducible calculi are associated to certain conjugacy classes in X and representations of isotropy groups. We find the full exterior algebras and show that they are inner by a bi-invariant 1-form θ which is a generator in the noncommutative de Rham cohomology H 1. The special cases where one subgroup is normal are analysed. As an application, we study the noncommutative cohomology on the quantum codouble D *(S 3)≅k(S 3) kℤ6 and the quantum double D(S 3) $$ > \triangleleft $$ k S 3, finding respectively a natural calculus and a unique calculus with H 0 = k.1. Kluwer Academic Publishers, 2004 quantum groups nationallicence Hopf algebras nationallicence group factorization nationallicence noncommutative geometry nationallicence bicovariant nationallicence cohomology nationallicence Ngakeu F. Institut de Mathématiques et de Sciences Physiques, BP 613, Porto-Novo, Benin aut Majid S. School of Mathematical Sciences, Queen Mary, University of London, 327 Mile End Rd, E1 4NS, London, UK aut Ezin J. Institut de Mathématiques et de Sciences Physiques, BP 613, Porto-Novo, Benin aut Acta Applicandae Mathematica Kluwer Academic Publishers 84/2(2004-11-01), 193-236 0167-8019 84:2<193 2004 84 10440 https://doi.org/10.1007/s10440-005-4592-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-005-4592-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ngakeu F. Institut de Mathématiques et de Sciences Physiques, BP 613, Porto-Novo, Benin aut NATIONALLICENCE 700 1- Majid S. School of Mathematical Sciences, Queen Mary, University of London, 327 Mile End Rd, E1 4NS, London, UK aut NATIONALLICENCE 700 1- Ezin J. Institut de Mathématiques et de Sciences Physiques, BP 613, Porto-Novo, Benin aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 84/2(2004-11-01), 193-236 0167-8019 84:2<193 2004 84 10440 NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-004-5592-6 text/html Onlinezugriff via DOI Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE NATIONALLICENCE NL-springer