Special and exceptional mock-Lie algebras

Abstract

We observe several facts and make conjectures about commutative algebras satisfying the Jacobi identity. The central question is which of those algebras admit a faithful representation (i.e., in Lie parlance, satisfy the Ado theorem, or, in Jordan parlance, are special).

v3: minor corrections

Cited by in corpus (10)

• The variety of dual mock-Lie algebras
• A characterisation of Lie algebras via algebraic exponentiation
• An effective criterion for Nielsen-Schreier varieties
• On the Kantor product, II
• The algebraic and geometric classification of antiassociative algebras
• On anticommutative algebras for which $[R_a,R_b]$ is a derivation
• On a pre-Jacobi-Jordan algebra: relevant properties and double construction
• On Bernstein algebras satisfying chain conditions II
• Algebraic constructions for Jacobi-Jordan algebras
• Representations and O-operators of Hom-(pre)-Jacobi-Jordan algebras