Cocommutative Hopf Algebras of Permutations and Trees
نویسندگان
چکیده
منابع مشابه
Cocommutative Hopf Algebras of Permutations and Trees
Consider the coradical filtration of the Hopf algebras of planar binary trees of Loday and Ronco and of permutations of Malvenuto and Reutenauer. We show that the associated graded Hopf algebras are dual to the cocommutative Hopf algebras introduced in the late 1980’s by Grossman and Larson. These Hopf algebras are constructed from ordered trees and heap-ordered trees, respectively. We also sho...
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The Calabi-Yau property of cocommutative Hopf algebras is discussed by using the homological integral, a recently introduced tool for studying infinite dimensional AS-Gorenstein Hopf algebras. It is shown that the skew-group algebra of a universal enveloping algebra of a finite dimensional Lie algebra g with a finite subgroup G of automorphisms of g is Calabi-Yau if and only if the universal en...
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The article is devoted to the describtion of quasitriangular structures (universal R-matrices) on cocommutative Hopf algebras. It is known that such structures are concentrated on finite dimensional Hopf subalgebras. In particular, quasitriangular structure on group algebra is defined by the pairs of normal inclusions of an finite abelian group and by invariant bimultiplicative form on it. The ...
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A standard heap ordered tree with n + 1 nodes is a finite rooted tree in which all the nodes except the root are labeled with the natural numbers between 1 and n, and that satisfies the property that the labels of the children of a node are all larger than the label of the node. Denote the set of standard heap ordered trees with n+1 nodes by Tn. Let kT = ⊕ n≥0 kTn. It is known that there are Ho...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2005
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-005-4628-y