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|<n|K|=|L| \lt n. Consider the subalgebra E 0=E 0(K,L)E_0 = E_0(K,L) in (n)\mathcal{M}(n) generated by all t l kt^k_l where either kKk \in K or lLl\in L (possibly both) and its subalgebra E 00E 0E_{00}\subset E_0 generated by all t l kt^k_l where both kKk \in K and lLl\in L Let t l kE 0t^{k'}_{l'} \notin E_0. Then for every eE 00e \in E_{00}, t l keet l kE 0t^{k'}_{l'} e - e t^{k'}_{l'} \in E_0.

The proof is the same and rather easy; the occurence of E 0E_0 in the second line of the proof is E 00E_{00}, in the rest E 0E_0 stays.

Proof of the main theorem of the paper

All as in the published version, everywhere E 0E_0 stays in the proof except that on should stay in the last paragraph that D L KD^K_L in fact belongs to the smaller subalgebra E 00E_{00} rather than E 0E_0, so it can serve as an input as ee in the Lemma 3.2.

Created on November 18, 2016 at 17:03:58. See the history of this page for a list of all contributions to it.