A ] 9 D ec 2 00 8 PARTIAL ( CO ) ACTIONS OF HOPF ALGEBRAS AND PARTIAL HOPF - GALOIS THEORY
نویسندگان
چکیده
We introduce partial (co)actions of a Hopf algebra H on an algebra. To this end, we introduce first the notion of lax coring, generalizing Wisbauer's notion of weak coring. We also have the dual notion of lax ring. Several duality results are given, and we develop Galois theory for partial H-comodule algebras.
منابع مشابه
Enveloping Actions for Partial Hopf Actions
Motivated by partial group actions on unital algebras, in this article we extend many results obtained by Exel and Dokuchaev [6] to the context of partial actions of Hopf algebras, according to Caenepeel and Jansen [3]. First, we generalize the theorem about the existence of an enveloping action, also known as the globalization theorem. Second, we construct a Morita context between the partial ...
متن کاملar X iv : 0 71 1 . 14 20 v 1 [ m at h . O A ] 9 N ov 2 00 7 Finite - dimensional Hopf C - bimodules and C - pseudo - multiplicative unitaries
Finite quantum groupoids can be described in many equivalent ways [8, 11, 16]: In terms of the weak Hopf C -algebras of Böhm, Nill, and Szlachányi [2] or the finite-dimensional Hopf-von Neumann bimodules of Vallin [14], and in terms of finite-dimensional multiplicative partial isometries [4] or the finite-dimensional pseudo-multiplicative unitaries of Vallin [15]. In this note, we show that in ...
متن کاملar X iv : m at h / 01 10 06 3 v 1 [ m at h . Q A ] 5 O ct 2 00 1 Integrals for ( dual ) quasi
A classical result in the theory of Hopf algebras concerns the uniqueness and existence of inte-grals: for an arbitrary Hopf algebra, the integral space has dimension ≤ 1, and for a finite dimensional Hopf algebra, this dimension is exaclty one. We generalize these results to quasi-Hopf algebras and dual quasi-Hopf algebras. In particular, it will follow that the bijectivity of the antipode fol...
متن کاملIntegrals, quantum Galois extensions and the affineness criterion for quantum Yetter-Drinfel’d modules
In this paper we shall generalize the notion of integral on a Hopf algebra introduced by Sweedler, by defining the more general concept of integral of a threetuple (H,A,C), where H is a Hopf algebra coacting on an algebra A and acting on a coalgebra C. We prove that there exists a total integral γ : C → Hom(C,A) of (H,A,C) if and only if any representation of (H,A,C) is injective in a functoria...
متن کاملM ay 2 00 2 Hopf Algebras of Dimension 14
Let H be a finite dimensional non-semisimple Hopf algebra over an algebraically closed field k of characteristic 0. If H has no nontrivial skew-primitive elements, we find some bounds for the dimension of H 1 , the second term in the coradical filtration of H. Using these results, we are able to show that every Hopf algebra of dimension 14, 55 and 77 is semisimple and thus isomorphic to a group...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008