Aspects of noncommutative differential geometry
Başlık çevirisi mevcut değil.
- Tez No: 402381
- Danışmanlar: PROF. CHRISTIAN LOMP
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2015
- Dil: İngilizce
- Üniversite: Universidade do Porto
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Matematik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 179
Özet
Özet yok.
Özet (Çeviri)
Hom-connections or noncommutative connections of the second type and associated integral forms have been introduced and studied by T.Brzezi ´nski as an adjoint version of the usual notion of a noncommutative connection in a right module over an associative algebra. A flat hom-connection on a differential calculus ( ;d) over an algebra A yields the integral complex which for various algebras has been shown to be isomorphic to the noncommutative de Rham complex (which is also termed the differential calculus in the context of quantum groups). We shed further light on the question when the integral and the de Rham complex are isomorphic for an algebra A with a flat hom-connection. We specialize our study to the case where an n-dimensional differential calculus can be constructed on a quantum exterior algebra over an A-bimodule. Criteria are given for free bimodules with diagonal or upper triangular bimodule structure. Our results are illustrated for a differential calculus on a multivariate quantum polynomial algebra and for a differential calculus on Manin's quantum n-space. Covariant Hom-bimodules, as a generalization of Woronowicz' covariant bimodules, are introduced and the structure theory of them in the Hom-setting, where (co)algebras have twisted (co)associativity and (co)unity conditions along with an associated endomorphism, is studied in a detailed way. These structural results about left-covariant and bicovariant Hom-bimodules were also restated in coordinate form. The category of bicovariant Hom-bimodules is proved to be a (pre-)braided monoidal category. The notion of Yetter-Drinfel'd Hom-module is presented and it is shown that the category of Yetter-Drinfel'd Hom-modules is a (pre-)braided tensor category as well. Finally, it is verified that these tensor categories are braided monoidal equivalent under certain conditions. The notions of Hom-coring, Hom-entwining structure and associated entwined Hommodule are introduced. A theorem regarding base ring extension of a Hom-coring is proven and then is used to acquire the Hom-version of Sweedler's coring. Motivated by a result of Brzezi´ nski, a Hom-coring associated to an Hom-entwining structure is constructed and an identification of entwined Hom-modules with Hom-comodules of this Hom-coring is shown. The dual algebra of this Hom-coring is proven to be a - twisted convolution algebra. By a construction, it is shown that a Hom-Doi-Koppinen datum comes from a Hom-entwining structure and that the Doi-Koppinen Hom-Hopf modules are the same as the associated entwined Hom-modules. A similar construction regarding an alternative Hom-Doi-Koppinen datum is also given. A collection of Hom- Hopf-type modules are gathered as special examples of Hom-entwining structures and corresponding entwined Hom-modules, and structures of all relevant Hom-corings are also considered. The definitions of first order differential calculus (FODC) on a monoidal Hom-algebra and left-covariant FODC over a left Hom-quantum space with respect to a monoidal Hom-Hopf algebra are given, and the left-covariance of a Hom-FODC is characterized. The extension of a FODC over a monoidal Hom-algebra to a universal Homdifferential calculus is described. The concepts of left-covariant and bicovariant FODC over monoidal Hom-Hopf algebras are introduced, and their associated right Homideals and quantum Hom-tangent spaces are studied. The notion of quantum (or generalized) Hom-Lie algebra of a bicovariant FODC over a monoidal Hom-Hopf algebra is obtained, in which generalized versions of antisymmetry relation and Hom-Jacobi identity are satisfied .
Benzer Tezler
- Asal halkaların belirli bazı genelleştirilmiş polinom ve fonksiyonel özdeşlikleri üzerine
On some certain polynomial and functional identities of prime rings
MÜNEVVER PINAR EROĞLU
- Noncommutative phase and the unitarization of the quantum group GLp,q(2)
Değişmeli olmayan faz operatörü ve GLp,q(2) kuantum grubunun üniterizasyonu
BURAK TEVFİK KAYNAK
Yüksek Lisans
İngilizce
2003
Fizik ve Fizik MühendisliğiBoğaziçi ÜniversitesiFizik Ana Bilim Dalı
PROF. DR. CİHAN SAÇLIOĞLU
- Değişmeli olmayan halkalar üzerinde tanımlı devirli kodlar
Cyclic codes over noncommutative rings
FATMANUR GÜRSOY
Yüksek Lisans
Türkçe
2013
MatematikYıldız Teknik ÜniversitesiMatematik Ana Bilim Dalı
PROF. DR. İRFAN ŞİAP
DOÇ. DR. BAHATTİN YILDIZ
- Asi nehri havzasında (Hatay) bulunan clarias gariepinus burchell, 1822 (karabalık)'un bazı biyolojik özellikleri
Aspects of some biology of clarias gariepinus burchell, 1822 (african catfish) in the Asi river (Hatay)
ŞÜKRAN YALÇIN
- İskenderun Körfezi'ndeki mavi yengeç (Callinectes sapidus RATHBUN, 1896)'in bazı biyolojik özellikleri
Aspects of the biology of blue crab (Callinectes sapidus RATHBUN, 1896)'in İskenderun Bay (Turkey)
CANAN TÜRELİ