Hopf-cyclic cohomology of bicrossed product Hopf algebras
Başlık çevirisi mevcut değil.
- Tez No: 400909
- Danışmanlar: DR. BAHRAM RANGIPOUR
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2012
- Dil: İngilizce
- Üniversite: University of New Brunswick
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 320
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Özet (Çeviri)
In this dissertation we study the coecients spaces (SAYD modules) of Hopfcyclic cohomology theory over a certain family of bicrossed product Hopf algebras, and we compute the Hopf-cyclic cohomology of such Hopf algebras with coecients. We associate a Hopf algebra, what we call a Lie-Hopf algebra, to any matched pair of Lie groups, Lie algebras and ane algebraic groups via the semidualization procedure of Majid. We then identify the SAYD modules over Lie-Hopf algebras with the representations and corepresentations of the total Lie group, Lie algebra or the ane algebraic group of the matched pair. First we classify the SAYD modules that correspond only to the representations of a total Lie group (algebra). We call them induced SAYD modules. We then generalize this identi cation, focusing on the matched pair of Lie algebras. We establish a one-to-one correspondence between the SAYD modules over the Lie-Hopf algebra associated to a matched pair of Lie algebras and certain SAYD modules over the total Lie algebra. Once the SAYD modules are associated to the representations and the corepiii resentations of Lie algebras, nontrivial examples can be constructed. This way, we illustrate a highly nontrivial 4-dimensional SAYD module over the Schwarzian Hopf algebra H1S. In addition, we discuss the periodic cyclic cohomology of Lie-Hopf algebras with nontrivial SAYD coecients. We obtain a general van Est isomorphism identifying the periodic cyclic cohomology of a Lie-Hopf algebra with the (relative) Lie algebra cohomology of the corresponding total Lie algebra.
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