2 5 N ov 2 00 8 MODULE CATEGORIES OVER POINTED HOPF ALGEBRAS
نویسنده
چکیده
We develop some techniques to the study of exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the small quantum groups uq(sl2).
منابع مشابه
ar X iv : 0 81 1 . 40 90 v 3 [ m at h . Q A ] 2 3 Ju n 20 09 MODULE CATEGORIES OVER POINTED HOPF ALGEBRAS
We develop some techniques for studying exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the small quantum groups uq(sl2).
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.
متن کاملAdjunctions between Hom and Tensor as endofunctors of (bi-) module category of comodule algebras over a quasi-Hopf algebra.
For a Hopf algebra H over a commutative ring k and a left H-module V, the tensor endofunctors V k - and - kV are left adjoint to some kinds of Hom-endofunctors of _HM. The units and counits of these adjunctions are formally trivial as in the classical case.The category of (bi-) modules over a quasi-Hopf algebra is monoidal and some generalized versions of Hom-tensor relations have been st...
متن کاملModule Categories over Pointed Hopf Algebras
We develop some techniques for studying exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the small quantum groups uq(sl2).
متن کامل