L-algebras and their ideals: from simplicity to semidirect products

2025/12/09 by Properzi, Silvia, Qin, Yufei
#03G25 #06D20 #Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2512.08579

Abstract

In this paper, we investigate the ideals of semidirect products of L-algebras and the structure of simple L-algebras. We provide a precise characterization of the ideals of semidirect products and describe the structure of their prime spectrum. Furthermore, we introduce a family of finite simple L-algebras and prove that every simple linear L-algebra belongs to this family. We also show that the family we construct coincides with the class of simple algebras in a certain subclass of finite CKL-algebras. As an application, we use these results to give a clear description of linear Hilbert algebras and their symmetric semidirect products.

Citations

• The prime spectrum of an L-algebra
• Groupes de Garside
• Gaussian Groups and Garside Groups, Two Generalisations of Artin Groups
• Artin-Gruppen und Coxeter-Gruppen

Related

• Ideals and Congruences in L-algebras and Pre-L-algebras
• Ideals and structure of operator algebras
• The prime spectrum of an L-algebra
• Semi-simple Leibniz algebras I
• Purely infinite simple C^*-algebras arising from free product constructions