Non-associative Frobenius algebras for simply laced Chevalley groups

DOI10.1090/tran/8484OpenAlexW3171809428MaRDI QIDQ5047903

Tom De Medts, Michiel Van Couwenberghe

Publication date: 17 November 2022

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.02625

zbMATH Keywords

Lie algebrasrepresentation theoryChevalley groupsFrobenius algebrasnon-associative algebrasaxial algebrasE8decomposition algebras

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Representation theory for linear algebraic groups (20G05) Representations of groups as automorphism groups of algebraic systems (20F29) Automorphisms, derivations, other operators (nonassociative rings and algebras) (17A36) Other nonassociative rings and algebras (17D99) Lie algebras and Lie superalgebras (17Bxx)

Cites Work

• Universal axial algebras and a theorem of Sakuma
• Jordan algebras and 3-transposition groups
• A simple construction for the Fischer-Griess monster group
• The friendly giant
• Zero weight spaces and the Springer correspondence
• The sum of generalized exponents and Chevalley's restriction theorem for modules of covariants
• Decomposition algebras and axial algebras
• SIMPLE GROUPS STABILIZING POLYNOMIALS
• A class of continuous non-associative algebras arising from algebraic groups including
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