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Results tagged with hopf-algebras
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user 3696
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 $G$.
2
votes
Accepted
Is every monomorphism of commutative Hopf algebras (over a field) injective?
It seems that Ben is nevertheless right that the answer to the first question is "NO". Let $G=SL(2,\Bbb C)$, and $B$ be the subgroup of lower triangular matrices. Then the inclusion $B\to G$ is an epi …
- 3,929
7
votes
Faithful characters of finite groups
Here is a short proof of the weaker version of the statement from Question 1 (giving a polynomial with rational coefficients). Let's think of characters as functions on conjugacy classes. Then $\chi(1 …
- 3,929
7
votes
Accepted
Comparing two similar procedures for quantizing a Casimir Lie algebra
The second construction (Lie bialgebra quantization) in fact also uses a Drinfeld associator. The braided tensor categories obtained in these two ways are equivalent, since the quasitriangular QUE alg …
- 3,929
8
votes
Accepted
Is there a canonical Hopf structure on the center of a universal enveloping algebra?
In the semisimple case, one has the Harish-Chandra isomorphism between the center ${\mathcal Z}(\mathfrak g)$ and $(S{\mathfrak h})^W$, where ${\mathfrak h}$ is a Cartan subalgebra of ${\mathfrak g}$ …
- 3,929