TL;DR
This paper investigates commutative algebras satisfying the Jacobi identity, focusing on which of these admit faithful representations, thus exploring their structural properties and representation theory.
Contribution
It presents new observations and conjectures about special and exceptional mock-Lie algebras, particularly regarding their faithfulness and representation capabilities.
Findings
Identifies conditions under which mock-Lie algebras are faithful
Proposes conjectures about the structure of special and exceptional cases
Highlights open questions in the representation theory of these 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).
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