Zoran Skoda quantum minor Ore erratum

Professor Tom Lenagan has alerted me of a misstatement in Lemma 3.2 of the published version,

• Every quantum minor generates an Ore set , (free-access link) International Math. Res. Notices 2008, rnn063-8; ,

that is the Lemma 2 of math.QA/0604610 v2 version. The correction is as follows:

Lemma 3.2 corrected

Let $|K|=|L| \lt n$. Consider the subalgebra $E_0 = E_0(K,L)$ in $\mathcal{M}(n)$ generated by all $t^k_l$ where either $k \in K$ or $l\in L$ (possibly both) and its subalgebra $E_{00}\subset E_0$ generated by all $t^k_l$ where both $k \in K$ and $l\in L$ Let $t^{k'}_{l'} \notin E_0$. Then for every $e \in E_{00}$, $t^{k'}_{l'} e - e t^{k'}_{l'} \in E_0$.

The proof is the same and rather easy; the occurence of $E_0$ in the second line of the proof is $E_{00}$, in the rest $E_0$ stays.

Proof of the main theorem of the paper

All as in the published version, everywhere $E_0$ stays in the proof except that on should stay in the last paragraph that $D^K_L$ in fact belongs to the smaller subalgebra $E_{00}$ rather than $E_0$, so it can serve as an input as $e$ in the Lemma 3.2.