One approach to identifying the C*-algebra of a product system over N^k is to build a representation of it with the aim of applying the Gauge-Invariant Uniqueness theorem. The main problem is how to build the representation. This is complicated by the commutativity of N^k - so many balanced tensor-product correspondences are isomorphic. I'll show how an abstract categorical result of Fowler-Sims can be used to surmount this obstacle. Joint work with Valentin Deaconu, Menevse Eryuzlu Paulovicks, and S. Kaliszewski.
Use of monoidal categories to generate representations of product systems over N^k Sponsored by the Meyer Fund
Thu, Apr. 23 11pm (MATH 220)
Functional Analysis
Roberto Hernandez Palomares (University of Waterloo)
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Spin models for singly-generated Yang-Baxter planar algebras are known to be determined by certain highly-regular classical graphs such as the pentagon or the Higman-Sims graph, which are extremely rare. Examples of spin models include the Jones and Kauffman polynomials. We will discuss the notion of higher-regularity for quantum graphs and give new examples of non-classical graphs yielding spin models. Time allowing, we will discuss some applications to quantum groups, topology and quantum information.
Quantum graphs and spin models Sponsored by the Meyer Fund
Use of monoidal categories to generate representations of product systems over N^k