R-matrices and Hopf Algebra Quotients
نویسنده
چکیده
We study a natural construction of Hopf algebra quotients canonically associated to an R-matrix in a finite dimensional Hopf algebra. We apply this construction to show that a quasitriangular Hopf algebra whose dimension is odd and square-free is necessarily cocommutative.
منابع مشابه
Hopf algebra structure on packed square matrices
We construct a new bigraded Hopf algebra whose bases are indexed by square matrices with entries in the alphabet {0, 1, . . . , k}, k > 1, without null rows or columns. This Hopf algebra generalizes the one of permutations of Malvenuto and Reutenauer, the one of k-colored permutations of Novelli and Thibon, and the one of uniform block permutations of Aguiar and Orellana. We study the algebraic...
متن کاملar X iv : m at h / 02 06 18 0 v 1 [ m at h . R A ] 1 8 Ju n 20 02 WHEN IS A SMASH PRODUCT SEMIPRIME ?
Miriam Cohen raised the question whether the smash product of a semisimple Hopf algebra and a semiprime module algebra is semiprime. In this paper we show that the smash product of a commutative semiprime module algebra over a semisimple cosemisimple Hopf algebra is semiprime. In particular we show that the central H-invariant elements of the Martindale ring of quotients of a module algebra for...
متن کاملOn the cyclic Homology of multiplier Hopf algebras
In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. We associate a cyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ consisting of a regular multiplier Hopf algebra $mathcal{H}$, a left $mathcal{H}$-comodule algebra $mathcal{R}$, and a unital left $mathcal{H}$-module $mathcal{X}$ which is also a unital algebra. First, we construct a para...
متن کاملAn Isomorphism for the Grothendieck Ring of a Hopf Algebra Order
If G is a finite abelian group, R is a principal ideal domain with field of quotients an algebraic number field K which splits G, and if A is a Hopf algebra order in KG, then the Grothendieck ring of the category of finitely generated A-modules is isomorphic to the Grothendieck ring of the category of finitely generated RG-modules. The Grothendieck group a£ of the category of finitely generated...
متن کاملA Note on Extending Hopf Actions to Rings of Quotients of Module Algebras
Given a Hopf algebra H and an H-module algebra A it is often important to be able of extending the H-action from A to a localisation of A. In this paper we are going to discuss sufficient conditions to extend Hopf actions as well as to characterise those localisations where the action can be extended. Our particular interest lies in the maximal ring of quotients of A.
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 2006