Lie Ideal Enhancements of Counting Invariants
Gillian Roxanne Grindstaff, Sam Nelson
TL;DR
This paper introduces a new enhancement to the quandle counting invariant for knots and links by utilizing Lie ideals within Lie algebra units, resulting in a stronger invariant than previous versions.
Contribution
It proposes a novel enhancement of the quandle counting invariant using Lie ideals in Lie algebra units, improving its discriminative power.
Findings
The enhancement is demonstrably stronger than the unenhanced invariant.
Examples show increased sensitivity in distinguishing knots and links.
The method integrates Lie algebra structures into knot invariants.
Abstract
We define enhancements of the quandle counting invariant for knots and links with a finite labeling quandle Q embedded in the quandle of units of a Lie algebra \mathfrak{a} using Lie ideals. We provide examples demonstrating that the enhancement is stronger than the associated unenhanced counting invariant.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research