2019/04/15 by Józiak, Paweł
#16T20 #20G42 Secondary: 81R50 #FOS: Mathematics #Operator Algebras (math.OA) #Primary: 46L89 #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1904.07721
We answer a question of A. Skalski and P.M. Sołtan (2016) about inner faithfulness of the S.~Curran's map of extending a quantum increasing sequence to a quantum permutation in full generality. To do so, we exploit some novel techniques introduced by Banica (2018) and Brannan, Chirvasitu, Freslon (2018) concerned with the Banica's conjecture regarding quantum permutation groups. Roughly speaking, we find a inductive setting in which the inner faithfulness of Curran's map can be boiled down to inner faithfulness of similar map for smaller algebras and then rely on inductive generation result for quantum permutation groups of Brannan, Chirvasitu and Freslon.