Work

Diagrammatic technique for Vogel’s universality

Year: 2026

Type: article

Abstract: In his 1999 preprint “Universal Lie Algebra”, P. Vogel put forward a hypothesis on the existence of a universal Lie algebra. Although this hypothesis remains open, it is known that many quantities in Lie theory admit universal descriptions. Remarkably, almost all such universal formulas have been obtained through the representation theory of simple Lie (super)algebras, whereas Vogel’s original framework was based on a more abstract diagrammatic algebra. Nevertheless, the diagrammatic approach has received little attention over the past two decades, since the last contributions by P.Vogel and J.Kneissler. In this work, we revive the diagrammatic technique grounded in Vogel’s $$\Lambda $$ Λ -algebra and show that it enables truly universal computations. We examine numerous examples and discuss them.

Source: The European Physical Journal C

DOI: 10.1140/epjc/s10052-026-16353-0

Authors: D. Khudoteplov, A. Sleptsov

Institutions: Moscow Institute of Physics and Technology, Kurchatov Institute, Institute for Information Transmission Problems, Institute for Theoretical and Experimental Physics

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Joint Institute for Nuclear Research

OpenAlex ID: W7161145907

FWCI:

Cites: 34

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Related to: 10