# L-infinity algebras, central extentions, and M-theory

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In this introduction for geometers and topologists, we explain the role that central extensions of L-infinity algebras, a concept we will define, plays in physics. This connection first appeared with the work of physicists D’Auria and Fré in 1982, but is beautifully captured by the “brane bouquet” of Fiorenza, Sati and Schreiber which shows how physical objects such as “strings”, “D-branes” and “M- branes” can be classified by taking successive central extensions of an especially simple L-infinity algebra called the “supertranslation algebra”.