Abstract
Easy quantum groups form a class of compact matrix quantum groups which are completely determined by set partitions. They have been defined in 2009 by Banica and Speicher in the orthogonal case (as quantum subgroups of Wang’s free orthogonal quantum group |$O_n^+$|). We extend their definition to the unitary case (as quantum subgroups of Wang’s free unitary quantum group |$U_n^+$|) using colored partitions. In the free case (i.e., restricting to noncrossing partitions), the corresponding categories of partitions have recently been classified by the authors by purely combinatorial means. We show how the quantum groups associated with them can be constructed from other known examples using generalizations of Banica’s free complexification. For doing so, we introduce new kinds of products between quantum groups.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
