# 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 $G$.

**9**

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### Is there a homotopy coherent analogue of Dieudonné modules?

**3**

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### Low dimensional noncommutative non-cocommutative Hopf algebras

**3**

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### Do chains send homotopy inverse limits of spaces to homotopy inverse limits of $E_\infty$-coalgebras?

**3**

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### Milnor exact sequence for homology of hopf algebras

**7**

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### The double cover in the classical limit of $U_q(\mathfrak{sl}_2)$

**2**

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### Primitive elements in Hopf algebras over the integers

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### Involutive solutions to the Yang-Baxter equation (and triangular Hopf algebras)

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### Superfluous axioms for ribbon Hopf algebra

**8**

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### Trying to understand “a refinement of the Peter–Weyl theorem” by Lusztig

**18**

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### Why does Drinfeld Unitarization work?

**2**

**1**answer

### About extensions between morphisms on the multiplier algebra

**1**

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### Non-degeneracy of comultiplication (multiplier Hopf algebras)

**1**

**1**answer

### Antipode on a multiplier Hopf-algebra

**2**

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### Examples of multiplier Hopf algebras

**1**

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### A comodule algebra map from a Hopf algebra to itself

**6**

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### Morphisms between compact quantum groups

**5**

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### Braided monoidal category, example

**3**

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### Show that a certain element is a linear combination of tensors

**4**

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### Hopf “algebroid” structure of a groupoid convolution algebra?

**3**

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### Is the kernel of an action of a Hopf algebra on an algebra a biideal?

**4**

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### Bialgebras with rigid representation theory

**4**

**1**answer

### References for Hopf Galois module theory

**5**

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### Deligne Tensor Product of Categories, Explicit Equivalence of $A\otimes_\mathbb{C} B\text{-Mod} \cong A\text{-Mod}\boxtimes B\text{-Mod}$

**3**

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### Galois descent of a Hopf algebra

**2**

**1**answer

### Definition of multiplier bialgebra

**13**

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### Question about definition of Hopf algebra in Hatcher

**4**

**1**answer

### Non-cosemisimple duals of pointed Hopf algebras

**2**

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### Hopf algebra with a non-grouplike invertible element

**4**

**1**answer

### Invertible elements of the Hopf algebra quantum $SU(2)$

**0**

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### Hopf algebra antipodes and right left comodule equivalences

**14**

**3**answers

### What is known about the category of Hopf algebras?

**3**

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### Derived category of an abelian monoidal category

**1**

**1**answer

### Example of a sub-bialgebra of a Hopf algebra that is not a Hopf subalgebra

**0**

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### Monoid objects constructed from duals

**3**

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### Is the category of Yetter-Drinfeld modules abelian?

**7**

**1**answer

### $\mathbb{Z}$-graded algebras and tensor products

**2**

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### Comodule Morita equivalence for Hopf algebras

**5**

**1**answer

### Comparing Hochschild (co)homology for algebras and coalgebras

**9**

**2**answers

### Definition of subcoalgebra over a commutative ring

**4**

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### Are the finite quantum permutation groups, weakly group-theoretical?

**4**

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### Categorical interpretation of the comodulus of a Hopf algebra?

**3**

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### Where can I find Drinfeld's original papers on quantum groups?

**5**

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### Simple quotients of a triple tensor product

**5**

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### Reference requests : Presentation of the braided dual of $U_q(\frak{sl_2})$

**5**

**1**answer

### Covariant splittings of Hopf algebra projections

**1**

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### When is the action of the braid group on tensor powers of Yetter-Drinfeld modules faithful?

**5**

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### Weak Hopf algebra structure on twisted group algebra

**6**

**2**answers

### Confusion around the reflection equation algebra

**2**

**1**answer

### Non-counital coalgebras

**11**

**3**answers