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Results tagged with quantum-groups
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user 98863
Questions about algebraic structures known as quantum groups, and their categories of representations. Quasitriangular Hopf algebras and their Drinfel'd twists, triangular Hopf algebras, $C^\star$ quantum groups, h-adic quantum groups, various semisimplified categories at roots of unity which are called "quantum groups", bicrossproduct quantum groups, and quantum groups coming from braided tensor categories.
4
votes
Coinvariants of tensor products of Hopf algebras
If $H$ is Hopf, then $H\otimes H$ with diagonal action is free, of the same dimension of $H$. The map is very explicit, you can surely can find it in any book of Hopf algebras (e.g. S. Montgomery). Th …
- 1,028
1
vote
Characters on Hopf algebras
Take an example of a finite dimensional Hopf algebra $A$, presented by generators and relations, generated by grouplikes and primitives. There are a lot of non-commutative non-cocommutative example …
- 7,746
3
votes
Classifications of Lie bialgebras
Sorry for the self publicity, but for the especific example of $gl_n(k)$, you can view it as $gl_n(k)\cong sl_n(k)\times k$ and we did some work for trivial central extensions that allow you to produc …
- 1,028
0
votes
A "concrete" example of a one-sided Hopf algebra
Did you try $B=k\{\dots,x_{-1},x_1,x_2,\dots, x_n,\dots \}/(x_nx_{n+1}-1: n\in\mathbb Z)$ with $\Delta x_n=x_n\otimes x_n$ for all $n$?
- 1,028
1
vote
Is $T(V) \rtimes T(V^* \otimes V)$ a bialgebra?
As @Zahlendreher said, the good language is that of bialgebras and comodule algebras so that you can do the bicross-product.
Identifying $V^*\otimes V\cong(End(V))^*=:C$ then $V$ is a right $C$-como …
- 1,028
1
vote
Alternative Definition of the Quantum Determinant?
If your Quantum (semi)group coacts on a finite dimensional Nichols algebra, then the top degree of the Nichols algebra is a 1-dimensional comodule, and so, it provides a group-like element that is the …
- 1,028
1
vote
Cotensoring by a Hopf Algebra
For any $H$-comodule $V$ you have its structure map $\rho:V\to V\otimes H$. The image of $\rho$ is the equalizer defining cotensor product.
- 1,028
2
votes
Braidings for Comodules of Co-quasi-triangular Hopf algebra
If $c:V\otimes V\to V\otimes V$ is a braiding on a finite dimensional vector space $V$ then $A=A(V,c)$, the FRT construction (equal to the free algebra on symbols $t_i^j$,
$i,j=1,\dots\dim V$, modulo …
- 1,028