Work

Universal weight systems from a minimal ℤ22-graded lie algebra

Year: 2025

Type: article

Abstract: Color Lie algebras, which were introduced by Ree, are a graded extension of Lie (super)algebras by an abelian group. We show that the color Lie algebras can be used to construct universal weight systems for knot invariants of Vassiliev and Kontsevich. As a simple example, we take [Formula: see text] as the grading group and consider the four-dimensional color Lie algebra called [Formula: see text]. The weight system constructed from [Formula: see text] is studied in some detail and some relations between the weights, such as the recurrence relation for chord diagrams, are derived. These relations show that the weight system from [Formula: see text] is a hybrid of those from [Formula: see text] and [Formula: see text].

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216525500452

Authors: N. Aizawa, Daichi Kimura

Institution: Osaka Metropolitan University

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Award: 次数付きリー代数の表現論に基づく可積分系の研究