ar X iv : m at h / 04 10 15 0 v 4 [ m at h . Q A ] 2 6 Ju n 20 05 CLASSIFICATION OF PM QUIVER HOPF ALGEBRAS
نویسندگان
چکیده
We give the classification of (co-)path Hopf algebras and semi-path Hopf algebras with pointed module structures. This leads to the classification of multiple crown algebras and multiple Taft algebras as well as pointed Yetter-Drinfeld kG-modules and the corresponding Nichols algebras. Moreover, we characterize quantum enveloping algebras in terms of semi-path Hopf algebras.
منابع مشابه
ar X iv : m at h / 04 10 15 0 v 6 [ m at h . Q A ] 1 9 Ju l 2 00 5 CLASSIFICATION OF PM QUIVER HOPF ALGEBRAS
We give the classification of (co-)path Hopf algebras and semi-path Hopf algebras with pointed module structures. This leads to the classification of multiple crown algebras and multiple Taft algebras as well as pointed Yetter-Drinfeld kG-modules and their corresponding Nichols algebras. Moreover, we characterize quantum enveloping algebras in terms of semi-path Hopf algebras.
متن کاملar X iv : m at h / 04 10 15 0 v 5 [ m at h . Q A ] 1 8 Ju l 2 00 5 CLASSIFICATION OF PM QUIVER HOPF ALGEBRAS
We give the classification of (co-)path Hopf algebras and semi-path Hopf algebras with pointed module structures. This leads to the classification of multiple crown algebras and multiple Taft algebras as well as pointed Yetter-Drinfeld kG-modules and the corresponding Nichols algebras. Moreover, we characterize quantum enveloping algebras in terms of semi-path Hopf algebras.
متن کاملar X iv : m at h / 04 10 15 0 v 8 [ m at h . Q A ] 1 5 A ug 2 00 5 CLASSIFICATION OF PM QUIVER HOPF ALGEBRAS
We give the classification of (co-)path Hopf algebras and semi-path Hopf algebras with pointed module structures. This leads to the classification of multiple crown algebras and multiple Taft algebras as well as pointed Yetter-Drinfeld kG-modules and their corresponding Nichols algebras. Moreover, we characterize quantum enveloping algebras in terms of semi-path Hopf algebras.
متن کاملar X iv : 0 90 6 . 34 15 v 1 [ m at h . Q A ] 1 8 Ju n 20 09 QUIVERS , QUASI - QUANTUM GROUPS AND FINITE TENSOR CATEGORIES
We study finite quasi-quantum groups in their quiver setting developed recently by the first author. We obtain a classification of finite-dimensional pointed Majid algebras of finite corepresentation type, or equivalently a classification of elementary quasi-Hopf algebras of finite representation type, over the field of complex numbers. By the Tannaka-Krein duality principle, this provides a cl...
متن کاملar X iv : m at h / 05 06 27 2 v 1 [ m at h . Q A ] 1 4 Ju n 20 05 A structure theorem for quasi - Hopf comodule algebras ∗
If H is a quasi-Hopf algebra and B is a right H-comodule algebra such that there exists v : H → B a morphism of right H-comodule algebras, we prove that there exists a left Hmodule algebra A such that B ≃ A#H . The main difference comparing to the Hopf case is that, from the multiplication of B, which is associative, we have to obtain the multiplication of A, which in general is not; for this w...
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