
TL;DR
This paper introduces a new algebraic structure called the bt-algebra of type B, providing foundational properties, representations, and link invariants relevant to knot theory in the solid torus.
Contribution
It constructs the first bt-algebra of type B, establishes a basis, a faithful tensorial representation, and demonstrates it supports a Markov trace for link invariants.
Findings
Established a basis for the bt-algebra of type B
Developed a faithful tensorial representation
Proved the algebra supports a Markov trace and derived link invariants
Abstract
We introduce a bt-algebra of type B. We define this algebra doing the natural analogy with the original construction of the bt-algebra. Notably we find a basis for it, a faithful tensorial representation, and we prove that it supports a Markov trace, from which we derive invariants of classical links in the solid torus.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models
