منابع مشابه
R-matrices and Hopf Algebra Quotients
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.
متن کاملHopf 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 کاملGorenstein global dimensions for Hopf algebra actions
Let $H$ be a Hopf algebra and $A$ an $H$-bimodule algebra. In this paper, we investigate Gorenstein global dimensions for Hopf algebras and twisted smash product algebras $Astar H$. Results from the literature are generalized.
متن کاملOn Quotients of Hopf Fibrations*
It was shown in [LV] that there are no PL-bundles of the form CPh ↪→ CPh → S where CPh denotes a PL-manifold homotopy equivalent to CP. It was stated at the end of [LV] that the homotopy analog of a) does not exist. In [U], Ucci showed that there exists no Hurewicz fibration of the form CP ↪→ CP → S. However, as stated, this was not the strongest possible result. Let HCP, HCaP and S h denote sp...
متن کاملBrick polytopes, lattice quotients, and Hopf algebras
This paper is motivated by the interplay between the Tamari lattice, J.-L. Loday’s realization of the associahedron, and J.-L. Loday and M. Ronco’s Hopf algebra on binary trees. We show that these constructions extend in the world of acyclic k-triangulations, which were already considered as the vertices of V. Pilaud and F. Santos’ brick polytopes. We describe combinatorially a natural surjecti...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2006
ISSN: 1073-7928,1687-0247
DOI: 10.1155/imrn/2006/47182