A Faithful Representation of the Singular Braid Monoid on Three Strands
Oliver T. Dasbach, Bernd Gemein
TL;DR
This paper proves the faithfulness of a specific linear representation of the singular braid monoid on three strands and provides a second solution to its word problem, motivated by group theory.
Contribution
It introduces a new faithful linear representation and a second group-theoretic solution to the word problem for the singular braid monoid on three strands.
Findings
The linear representation is faithful.
A second solution to the word problem is provided.
The methods are group-theoretically motivated.
Abstract
We show that a certain linear representation of the singular braid monoid on three strands is faithful. Furthermore we will give a second - group theoretically motivated - solution to the word problem in this monoid.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic structures and combinatorial models · semigroups and automata theory