# Questions tagged [hopf-algebras]

A Hopf algebra is a vector space $H$ over a field $k$ endowed with an associative product $\times:H\otimes_k H\to H$ and a coassociative coproduct $\Delta:H\to H\otimes_k H$ which is a morphism of algebras. Unit $1:k\to H$, counit $\epsilon:H\to k$ and antipode $S:H\to H$ are also required. Such a structure exists on the group algebra $k G$ of a finite group $G$.

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### Characterizing discrete quantum groups

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### Coinvariants of tensor products of Hopf algebras

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### Integrals and finite dimensionality in braided Hopf algebras

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### Hopf algebras structure and quantum affine algebras

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### Quantum analogue of certain property of compact groups

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### On reflexive bialgebras

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### Abelian category from the category of Hopf algebras

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### Irreducibility of product bicomodules

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### Is $Tor_A(k,k)$ a bicommutative Hopf algebra?

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### Tensor algebras in the bicategory $\mathsf{2Vect}$

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### What is a quantum analogue of the fact that the second fundamental group of every Lie group is trivial?

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### Reduced compact quantum group and left and right multiplication

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### Corepresentations on Hilbert modules

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### Rigidity for the category of comodules over a Hopf algebra

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### Tensor product of fields 2

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### Classification of $\operatorname{Rep}D(H)$

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### Relative projectivness and tensor products

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### Update on “Hopf algebras: their status and pervasiveness” by Hazewinkel

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### W H Lin's thesis and Hopf subalgebras of the Steenrod algebra

**2**

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### A weaker version of strongly graded algebras

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### Characters on Hopf algebras

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### Representations of $D(G)$ as an object in the center of $\operatorname{Rep}(G)$

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### Intuitive, elementary intros to Hopf algebras/monoids

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### Classification of $\operatorname{Rep} D(G)$

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### Submodules of $V\otimes V^*$

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### Subfunctor of internal Hom

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### Embedding problems on quantum groups？

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### Integrals in noncommutative graded algebras which are not necessarily Hopf

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### Comultiplication of elements of partition of unity

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### Example of a commutative, cocommutative, $p$-torsion Hopf algebra which is dualizable but not self-dual?

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### “Nice” bases for finite dimensional semisimple Hopf algebras

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### Weakly reflexive algebra vs proper (residually finite-dimensional) algebra

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### Images and Kernels of tensor products of homomorphisms of modules

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### What properties of a finite group fibre functor give its endomorphisms a hopf algebra structure?

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### Tannaka-Krein duality in Chari-Pressley's book

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### Noncrossing partitions in Hopf algebras/monoids via compositional inversion

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### Classification of one dimensional (non-commutative) formal group laws over $k[\epsilon]/(\epsilon^n)$

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### Cobraided and coquasitriangular Hopf algebras

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### When is $N^{*} \otimes_K M$ projective for a local Hopf algebra?

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### Some quantities associated to finite dimensional Hopf algebras

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### Examples of basic coalgebras

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### The relationship between representations of groups and evaluation and coevaluation maps for $vect_{G}$ module categories

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### Hopf structure on the universal enveloping of a super Lie algebra

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### The tensor product of two monoidal categories

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### Image of Comultiplication on Finite Quantum Groups/Hopf Algebras

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### Is there a way to adjoin a counit to a non counital coalgebra?

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### Invariance of Finite Dimensional Woronowicz $\mathrm{C}^*$-ideals under the Antipode

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### Milnor-Moore and the characteristic zero homology of H-spaces

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### Noncommutative Leray - Hirsch theorem in the context of noncommutative principal bundles

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