# 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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### Explicit examples of finite dimensional, involutive Hopf algebras with traceless antipode?

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### Functoriality of the Hopf dual

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### It there a nice way to describe the structure of Malcev-complete groups?

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### Is there another quantum deformation of sl(2)?

**6**

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### Modules over Hopf Algebras and $E_2$-algebras

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### How are the unit/counit of a Hopf algebra and of an categorical adjunction related?

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### Independence of characters with respect to polynomials

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### Lie algebra of a compact Lie group

**3**

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### Tannaka-Krein reconstruction and rigidity

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### Hopf algebra interpretation of hypergraph duality?

**16**

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### Lang's Jacobian identity: slicker, elementary proof?

**13**

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### Hopf dual of the Hopf dual

**4**

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### The Ungraded Milnor-Moore Theorem

**3**

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### When is this map of Hopf algebras Surjective?

**11**

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### Unbiased Hopf algebras

**8**

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### The dual of a dual in a rigid tensor category

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### Free module over $H$-module algebra

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### Quasi-symmetric generalizations of classical symmetric functions

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### Is there a ''simple'' formula for the inverse of the Drinfeld associator?

**7**

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### Hopf Subalgebras of Quantized Algebras

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### What additional property does the antipode give on the category of all modules over an Hopf algebra?

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### Module algebras and comodule algebras

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### Exceptional Quantum Groups as FRT-Algebras

**2**

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### For any finite-dimensional Hopf C*-algebra, can one make the multiplication and co-multiplication cyclically symmetric simultanously?

**1**

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### When is a Frobenius Algebra a Quasi-Frobenius Ring?

**7**

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### On the isomorphism problem of enveloping algebras

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### $Q(f+g)_*=Q(f_*+g_*)$ (The maps induced by the sum is the sum of induced maps modulo decomposables [Reference request]

**5**

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### A diagram for understanding action/coaction compatibility in a Yetter-Drinfeld module

**5**

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### Are there examples of finite-dimensional weak Hopf C*-algebras with non-involutive antipode?

**11**

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### Hopf-Galois extensions where the “extension” is a module?

**6**

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### Group schemes over ring of Witt vectors and their representing algebras

**2**

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### turning left modules into right modules over bialgebroids

**6**

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### The difference between $q$-deformations and $h$-deformations

**2**

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### Quantum invariant: The canonical $2$-tensor

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### Detecting skew-primitives in representation categories

**2**

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### Relative version of Hopf cyclic cohomology

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### Algebras for (Koszul) Hopf operads

**6**

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### Inner automorphisms of Hopf algebras

**3**

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### What are the primitive elements in a polynomial Hopf algebra with primitive indeterminates?

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### Category of (co)commutative Hopf monoids in an exact category

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### Name for the action of a bialgebra on an algebra

**2**

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### Looking for an automorphism constructed from Hopf algebraic data

**17**

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### Stable homotopy type theory?

**3**

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### Number of Isomorphism Classes of Corepresentations of A Compact Quantum Group

**16**

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### Examples of representations of quantum groups

**2**

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### group action on Tor groups of modules and smash product

**13**

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### Analog of Haar element in an algebra

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### The order of the antipode in a Hopf algebra

**8**

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### Categorical interpretation of quantum double $D(A,B,\eta)$

**2**

**1**answer