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Algebraic functor calculus and commutator theory

Abstract : Classically, Lie algebras can be considered as linearizations of groups in several ways, and thus provide key tools in group theory. With the emergence of more and more other non-linear algebraic structures the problem arises to generalize the relations between groups and Lie algebras to a much broader context. A categorical approach to this problem will be presented starting out from a new notion of commutator and lower central series deduced from the cross-effects of the identity functor. Lie algebras then generalize to algebras over linear or, more generally, multilinear functor operads.
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Submitted on : Tuesday, March 23, 2021 - 11:52:20 AM
Last modification on : Tuesday, October 19, 2021 - 6:38:17 PM

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  • HAL Id : hal-03177595, version 1

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Manfred Hartl. Algebraic functor calculus and commutator theory. Kolloquium über Reine Mathematik, May 2013, Hambourg, Germany. ⟨hal-03177595⟩

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