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Theodore Voronov: Canonical and (higher) derived brackets

Tid: To 2025-02-13 kl 10.30 - 11.30

Plats: Zoom

Videolänk: Meeting ID: 921 756 1890

Medverkande: Theodore Voronov, Manchester University

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Abstract

 Bracket structures in differential geometry fall into two classes. (1) There are canonical, i.e., natural brackets that do not require any extra structure for their definition. An example of them is the commutator of vector fields (whose non-commutative version is the Gerstenhaber bracket of multilinear functions). Other examples are given by Poisson and Schouten brackets (of Hamiltonians and multivector fields respectively). (2) A different class of brackets arises as “derived” from a canonical bracket and some “generating” or “master” element that self-commutes with respect to the initial bracket. There is a general algebraic construction of higher derived brackets, which produces L-infinity algebras from simple data. (And all L-infinity algebras arise this way.) The talk will be a pedagogical recollection of my old work, and depending on how it goes, there may be some follow-up talks.