A topological origin of quantum symmetric pairs
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T. A. N. Weelinck [1]
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[1] University of Edinburgh
University of Edinburgh
Reino Unido
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- Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 3, 2019
- Idioma: inglés
- Enlaces
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Resumen
It is well known that braided monoidal categories are the categorical algebras of the little two-dimensional disks operad. We introduce involutive little disks operads, which are [Math Processing Error]-orbifold 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 anti-involution together with a pointed module category carrying a universal solution to the (twisted) reflection equation. Examples of these are obtained from the categories of representations of a ribbon Hopf algebra with an involution and a quasi-triangular coideal subalgebra, such as a quantum group and a quantum symmetric pair coideal subalgebra.
