A topological origin of quantum symmetric pairs
Abstract
It is well known that braided monoidal categories are the categorical algebras of the little twodimensional disks operad. We introduce involutive little disks operads, which are Z/2Zorbifold versions of the little disks operads. We classify their categorical algebras and describe these explicitly in terms of a finite list of functors, natural isomorphisms and coherence equations. In dimension two, the categorical algebras are braided monoidal categories with an antiinvolution together with a pointed module category carrying a universal solution to the (twisted) reflection equation. Main examples are obtained from the categories of representations of a ribbon Hopf algebra with an involution and a quasitriangular coideal subalgebra, such as a quantum group and a quantum symmetric pair coideal subalgebra.
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1804.02315
 Bibcode:
 2018arXiv180402315W
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Category Theory
 EPrint:
 41 pages, 12 figures