Path Hopf Algebras and Co-path Hopf Algebras
نویسندگان
چکیده
The main goal is to study the Hopf algebra structure on quivers. The main result obtained by C. Cibils and M. Rosso is improved. That is, in the case of infinite dimensional isotypic components it is shown that the path coalgebra kQ admits a graded Hopf algebra structure if and only if Q is a Hopf quiver. All nonisomorphic point path Hopf algebras and point co-path Hopf algebras are found. The relation between path algebras and path coalgebras is given. It is proved that Taft algebras and multiple Taft algebras are Hopf subalgebras of crown algebras and multiple crown algebras, respectively. 2000 Mathematics subject Classification: 16w30, 16G10.
منابع مشابه
0 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 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 4 [ m at h . Q A ] 2 6 Ju n 20 05 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 : 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.
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