Work

Solid lines in axial algebras of Jordan type \tfrac{1}2 and Jordan algebras

Year: 2025

Type: article

Abstract: We show that a primitive axial algebra of Jordan type 1 2 \tfrac {1}{2} is a Jordan algebra if and only if every 2 2 -generated subalgebra is solid , a notion introduced recently by Ilya Gorshkov, Sergey Shpectorov and Alexei Staroletov. As a byproduct, we show that a subalgebra generated by axes a , b a,b is solid if and only if the associator [ L a , L b ] [L_a,L_b] is a derivation. Moreover, we show that 2 2 -generated subalgebras that are not solid contain precisely 3 3 axes.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17111

Author: Jari Desmet

Institution: Ghent University

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Fonds Wetenschappelijk Onderzoek

Award: Non-associative algebras for exceptional groups