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Since locally compact quantum groups date no later than the late 1980's, then how does this count as "relatively new"? Figaro 00:54, 17 December 2005 (UTC)
The current definition of locally compact quantum groups (which is what is usually meant by that term) was given by Vaes and Kustermans in 1999, which is relatively recent. It is true that the multiplicative unitary approach predates the work of V&K by several years, but the consensus (at least at the moment) seems to be that the definitive definition is the newer one HrHolm 11:56, 23 December 2005 (UTC)