Search Results

Consider the algebra (I am for forgetting the Hopf structure) $U_q(\frak{sl}_2)$ defined over ${\mathbb C}$, and the formal power series version/ $h$-adic version $U_h(\frak{sl}_2)$, which I think as …

Let $A$ be an algebra, $H$ a Hopf algebra, and $$ \beta_A: A \to A \otimes H, ~~~~~ a \mapsto a^{(1)} \otimes a^{(2)} $$ a right $H$-coaction. This induces a right $H$-coaction on $A \otimes A$ defin …

This is a reasonably known result. That $S(u^1_i)u^j_1 = q^{-1}u^j_1S(u^1_i)$, was originally proven (to the best of my knowdledge) in FRT's '89 paper "Quantum Groups and Lie Algebras" - the paper is …

I tried to find a resolution of this problem by looking at it in the greater generality of FRT-algebras. However, I also ran into an apparent contradiction. I have posted my calculations as a new ques …

Can anyone give an explicit basis of the universal (noncommutative) differential calculus over an algebra $A$ with basis ${e_i}$. (The universal calculus over $A$ is the kernel of the multiplication m …

For quantum $\operatorname{SU}(2)$, Woronowicz gave a well differential calculus. If we denote the generators of quantum $\operatorname{SU}(2)$ by $a$, $b$, $c$, $d$, then the ideal of $\ker(\epsilon) …

I have recently begun to study quasi-triangular structures and have come across a problem I can't resolve. Let ${\cal U}_q({\mathfrak sl}_N)$ denote the quantised enveloping algebra of ${\mathfrak sl} …

Let $V$ be a finite dimensional vector space and let $R$ be a linear invertible mapping from $V \otimes V$ to itself. If we fix a basis $\{e_i\}_{i=1,2, \cdots ,n}$ then we have $N^4$ complex numbers …

As is well known, the set $\{a^ib^jc^k | i,j,k \in \mathbb{Z}\_{\geq 0},k>0\} \cup \{b^lc^md^n | l,m,n \in \mathbb{Z}\_{\geq 0}\}$ forms a basis for quantum $SU(2)$. Does anyone know of a basis for …

Let $(\Omega,d)$ be a differential calculus over an algebra $A$. It is easy to show that $\Omega$ is always equal to a quotient of $\Omega_u(A)$, the universal calculus over $A$, by some ideal $N$ of …

In a comment for this old question, it was said that > There is a theorem that Hopf modules are (up to isomorphism) the tensor products of their coinvariants with H. (This theorem is usually worded …

When Grothendieck and his followers were working on their profound progress of algebraic geometry, did they ever consider non-commutative rings? Is there anyway evidence that Grothendieck foresaw the …