Homotopy Lie Algebras

Matthew Peddie

Frank Adams 2,

Gauge symmetries of a mechanical system are equivalent mathematical descriptions of the same physics. Generators of these symmetries form an open Lie algebra, a Lie algebra which is a Lie algebra up to some equations that we don't care about. In this context physicists discovered homotopy algebras, algebras in which the properties hold up to elements we don't care about.
 
I'll provide some motivation for considering these algebras, the definition and some examples.
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