Two different models for a Hopf-von Neumann algebra of bounded functions on the quantum semigroup of all (quantum) permutations of infinitely many elements are proposed, one based on projective limits of enveloping von Neumann algebras related to finite quantum permutation groups, and the second on a universal property with respect to infinite magic unitaries.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-7,
author = {Debashish Goswami and Adam Skalski},
title = {On two possible constructions of the quantum semigroup of all quantum permutations of an infinite countable set},
journal = {Banach Center Publications},
volume = {97},
year = {2012},
pages = {199-214},
zbl = {1272.81097},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-7}
}
Debashish Goswami; Adam Skalski. On two possible constructions of the quantum semigroup of all quantum permutations of an infinite countable set. Banach Center Publications, Tome 97 (2012) pp. 199-214. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-7/