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Status of the analog of the Haar measure on quantum groups

+ 8 like - 0 dislike
2097 views

In (Masuda, Nakagami, Woronowicz)'s paper, in the introduction, the authors mentioned the deficiency common to both their and (Kusterman, Vaes)'s approach regarding the Haar state (or Haar measure analog). The deficiency is that they had to presuppose existence when one would expect to derive it. The existence can be proven for compact quantum groups, where a multiplicative unit is assumed.

My question: What is the current status on this? Has the existence of the Haar measure analog been derived or is it still an axiom? The papers are not that recent, so maybe they achieved it.

A bonus question: What about Haar systems for locally compact quantum groupoids? are they an axiom?


This post imported from StackExchange MathOverflow at 2014-10-01 22:43 (UTC), posted by SE-user Henrique Tyrrell

asked Sep 23, 2014 in Mathematics by Henrique Tyrrell (40 points) [ revision history ]
edited Oct 1, 2014 by Dilaton
I'm only a spectator of LCQG stuff, but my impression is that this is still open.

This post imported from StackExchange MathOverflow at 2014-10-01 22:43 (UTC), posted by SE-user Yemon Choi
If is necessarily an axiom, what then? What would it mean? A revision of the topological Hopf structures in order to derive the existence would be needed? Or only "Haar Quantum groups" should be studied? I'm sorry for being so demanding.

This post imported from StackExchange MathOverflow at 2014-10-01 22:43 (UTC), posted by SE-user Henrique Tyrrell
Henrique, I'm afraid this is where I'd have to defer to an expert, but there are some people who would know and who are occasionally on MO

This post imported from StackExchange MathOverflow at 2014-10-01 22:43 (UTC), posted by SE-user Yemon Choi
So let us hope this question shows up to them.

This post imported from StackExchange MathOverflow at 2014-10-01 22:43 (UTC), posted by SE-user Henrique Tyrrell
I edited your tags since qa.quantum algebra seems to be more for the algebraic side and really this question is aimed at people who know about Kustermans-Vaes / Woronowicz /etc

This post imported from StackExchange MathOverflow at 2014-10-01 22:43 (UTC), posted by SE-user Yemon Choi
It's ok. I mentioned QA because of Arxiv's category.

This post imported from StackExchange MathOverflow at 2014-10-01 22:43 (UTC), posted by SE-user Henrique Tyrrell

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