Cartan calculus for quantum differentials on bicrossproducts |
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Authors: | F Ngakeu S Majid J -P Ezin |
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Institution: | (1) Institut de Mathématiques et de Sciences Physiques, BP 613 Porto-Novo, Benin;(2) School of Mathematical Sciences, Queen Mary, University of London, 327 Mile End Rd, E1 4NS London, UK |
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Abstract: | 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 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)
k6 and the quantum double D(S
3)
k
S
3, finding respectively a natural calculus and a unique calculus with H
0 = k.1. |
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Keywords: | quantum groups Hopf algebras group factorization noncommutative geometry bicovariant cohomology |
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