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Classification of thin Jordan schemes
Muzychuk, Mikhail1; Pech, Christian2; Woldar, Andrew3
1Ben Gurion University of the Negev, Beer Sheva, Israel
2Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic
3Villanova University, Villanova, PA, USA
Algebraic Combinatorics, Volume 9 (2026) no. 3, pp. 811-830

Jordan schemes generalize association schemes in a manner similar to how Jordan algebras generalize associative algebras. It is well known that association schemes of maximum rank are in one-to-one correspondence with groups (so-called thin schemes). In this paper, we classify Jordan schemes of maximum rank-to-order ratio and show that regular Jordan schemes of such type correspond to a special class of Moufang loops known as ring-alternative loops.

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DOI: 10.5802/alco.489
Classification: 17C50, 20N05, 05E30, 05E16, 16W10
Keywords: Jordan algebra, thin Jordan scheme, coherent configuration, Moufang loop, RA-loop, autonomous

Muzychuk, Mikhail  1 ; Pech, Christian  2 ; Woldar, Andrew  3

1 Ben Gurion University of the Negev, Beer Sheva, Israel
2 Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic
3 Villanova University, Villanova, PA, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Muzychuk, Mikhail; Pech, Christian; Woldar, Andrew. Classification of thin Jordan schemes. Algebraic Combinatorics, Volume 9 (2026) no. 3, pp. 811-830. doi: 10.5802/alco.489
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