Quantum diagrammatics for \(F_4\)
type: Item
instance of: scholarly article
title: Quantum diagrammatics for \(F_4\)
zbMATH Open document ID: 1544.18023
author: Alistair Savage
author: Bruce W. Westbury
published in: Journal of Pure and Applied Algebra
publication date: 2024-07-01T00:00:00Z
review text: In [Bull. Lond. Math. Soc. 55, No. 1, 349--374 (2023; Zbl 1519.18010)] \textit{R. Gandhi} et al. defined a diagrammatic monoidal category, together with a full and essentially surjective monoidal functor from this category to the category of modules over the exceptional Lie algebra of type \(F_4\). Thus, obtaining a set of diagrammatic tools for studying type \(F_4\) representation theory analogous to those of the oriented and unoriented Brauer categories in classical type.\N\NThe authors of the paper under review generalize the work in [loc. cit.] by developping a quantum version of the diagrammatics. Precisely, they introduce a graphical calculus for the representation theory of the quantized enveloping algebra of type \(F_4\). This is achieved by diagrammatic description of the category of invariant tensors on the 26-dimensional fundamental representation.
reviewed by: Mohamed Elhamdadi
Mathematics Subject Classification ID: 18M15
Mathematics Subject Classification ID: 18M30
Mathematics Subject Classification ID: 17B25
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 7873756
zbMATH Keywords: monoidal category
zbMATH Keywords: string diagram
zbMATH Keywords: quantized enveloping algebra
zbMATH Keywords: exceptional Lie algebra
zbMATH Keywords: \(F_4\)
zbMATH Keywords: link invariant
MaRDI profile type: Publication
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DOI: 10.1016/J.JPAA.2024.107731
description: scientific article; zbMATH DE number 7873756