Multiplicative isomorphisms and derivations on axial algebras

Multiplicative isomorphisms and derivations on axial algebras

In this paper, we show that the multiplicative derivations on J(α)-axial algebras, with α≠1,0,12, are additive under suitable conditions, which nowadays are called Martindale-type conditions. Besides, with proper assumptions, we proceed to study the additivity of multiplicative isomorphisms and deri...

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Veröffentlicht in:Journal of pure and applied algebra 2024-12, Vol.228 (12), p.107753, Article 107753
Hauptverfasser: Ferreira, Bruno L.M., de Araujo Smigly, Douglas, Barreiro, Elisabete
Format: Artikel
Sprache:eng
Schlagworte:
Additivity
Axes
Axial algebras
Fusion rule
Multiplicative maps
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Zusammenfassung:In this paper, we show that the multiplicative derivations on J(α)-axial algebras, with α≠1,0,12, are additive under suitable conditions, which nowadays are called Martindale-type conditions. Besides, with proper assumptions, we proceed to study the additivity of multiplicative isomorphisms and derivations in the context of M(α,β)-axial algebras, except for multiplicative derivations when β=12. In this case, we mention a research question at the end.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2024.107753