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Local representations of the loop braid group. (English) Zbl 1430.20006

Summary: We study representations of the loop braid group \(LB_n\) from the perspective of extending representations of the braid group \(\mathcal{B}_n\). We also pursue a generalization of the braid/Hecke/Temperlely-Lieb paradigm – uniform finite dimensional quotient algebras of the loop braid group algebras.

MSC:

20C08 Hecke algebras and their representations
16T25 Yang-Baxter equations
20F36 Braid groups; Artin groups
57K10 Knot theory
81R05 Finite-dimensional groups and algebras motivated by physics and their representations

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