Work

A Two-Dimensional Counterexample to Radical Equality in Primitive Axial Algebras

Year: 2022

Type: preprint

Abstract: In this article, we develop a further adaptation of the method of Skjelbred-Sund to construct central extensions of axial algebras. We use our method to prove that all axial central extensions (with respect to a maximal set of axes) of complex simple finite-dimensional Jordan algebras are split and that all non-split axial central extensions of dimension $n\leq 4$ over an algebraically closed field of characteristic not $2$ are Jordan. Also, we give a classification of $2$-dimensional axial algebras and describe some important properties of these algebras.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2211.00334

Authors: Kaygorodov, Ivan, González, Cándido Martín, Páez-Guillán, Pilar

Institution: Universidad de Málaga

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Austrian Science Fund, Ministerio de Ciencia e Innovación, Russian Science Foundation, Xunta de Galicia, Junta de Andalucía, Fundação para a Ciência e a Tecnologia, Agencia Estatal de Investigación

Awards: G102544051, G11420688, G1321705011, G1496055848, G2291076443, G3233984796, G33107482, G3332366440, G4242938006, G5296777416, G552830540, G5805502524, G6057752954, Affine geometry on Lie groups and Lie-algebraic structures, G8814747429

OpenAlex ID: W4308021858

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