Commutative combinatorial Hopf algebras
نویسندگان
چکیده
منابع مشابه
Commutative combinatorial Hopf algebras
We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures and investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general construction based on graphs, and its noncommutative dual is realized in three different ways, in particular, as the Grossman–Larson algebra of heap-ordered trees. ...
متن کاملActions of Commutative Hopf Algebras
We show that actions of finite-dimensional semisimple commutative Hopf algebras H on //-module algebras A are essentially group-gradings. Moreover we show that the centralizer of H in the smash product A # H equals A" ® H. Using these we invoke results about group graded algebras and results about centralizers of separable subalgebras to give connections between the ideal structure of A, A and ...
متن کاملCombinatorial Hopf Algebras and Towers of Algebras
Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras L n≥0 An can be endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap, and independently Lam and Shimozono constructed dual graded graphs from primitive elements in Hopf algebras. In this paper we apply the composition of these constructions to towers of al...
متن کاملCombinatorial Hopf algebras from PROs
We introduce a general construction that takes as input a so-called stiff PRO and that outputs a Hopf algebra. Stiff PROs are particular PROs that can be described by generators and relations with precise conditions. Our construction generalizes the classical construction from operads to Hopf algebras of van der Laan. We study some of its properties and review some examples of application. We g...
متن کاملHigher Conjugation Cohomology in Commutative Hopf Algebras
We study the action of the symmetric group Σn on a tensor product of n − 1 copies of a commutative Hopf algebra A, defined by the second author [8]. We show that for ‘nice’ Hopf algebras, the cohomology algebra H∗(Σn;A⊗n−1) is independent of the coproduct if n.(n − 2)! is invertible in the ground ring. Let A be a graded, connected, unital, counital, associative, coassociative Hopf algebra. In s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2007
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-007-0077-0