Solutions of the braid equation and orders

2017/01/06 by Jorge Alberto Guccione, Guccione, Jorge Alberto, Juan José Guccione +3
Mathematics · #16T25 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16T25

paper · pdf · doi:10.48550/arxiv.1701.01752

29 pages

arxiv created 2017/01/06 · arxiv updated 2017/01/10

Abstract

We introduce the notion of a non-degenerate solution of the braid equation on the incidence coalgebra of a locally finite order. Each one of these solutions induce by restriction a non-degenerate set theoretic solution over the underlying set. So, it makes sense to ask if a non-degenerate set theoretic solution on the underlying set of a locally finite order extends to a non-degenerate solution on its incidence coalgebra. In this paper we begin the study of this problem.

Related

• Solutions of the Braid Equation with set-type square
• Unprovability results involving braids
• Set theoretic solutions of the Yang-Baxter equation, graphs and\n computations
• Cocommutative q-cycle coalgebra structures on the dual of the truncated polynomial algebra
• On representations of braid groups determined by directed graphs