# Questions tagged [combinatorial-hopf-algebras]

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### Hopf algebra interpretation of hypergraph duality?

The work of Aguiar and Ardila (https://arxiv.org/abs/1709.07504) on Hopf monoids for generalized permutohedra gives a Hopf monoid structure on the collection of hypergraphs; see sections 19 and 20 of ...
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### Is Leray's theorem on commutative Hopf algebras proven in Milnor-Moore?

Question 1. Is a correct proof of Leray's theorem (the one that says that a connected graded Hopf algebra $H$ over a field of characteristic $0$ is isomorphic as an algebra to the symmetric ...
210 views

### Hopf structures on “pictorial” descriptions of permutations

There is a well-known Hopf structure on permutations, due to Malvenuto and Reutenauer. Here, the F basis elements are permutations in one-line notation, the product of two permutations is their ...
235 views

### Problem with Eisenbud's Lemma “Symmetry of Diagonalization”?

This question was first asked on MathSE but nobody answered. In his proof of Lemma A2.5 in his book Commutative Algebra with a View towards Algebraic Geometry, Prof. Eisenbud writes something like ...
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### Classification of Hopf algebras (state of the art)

I assume that the classification of (certain families of) Hopf algebras is still an open problem, am I right? My question is the following: What is the current state of the art? What is known about ...
Let $k$ be a field of characteristic $0$. Let $H$ be a cocommutative connected filtered bialgebra over $k$. ("Connected" means that the counit, restricted to the $0$-th part of the filtration, is an ...
Let $k$ be a commutative ring with $1$, and let $V$ be a $k$-module. Let $TV$ be the $k$-module $\bigoplus\limits_{n\in\mathbb N}V^{\otimes n}$, where all tensor products are over $k$. We define a $k$...