Geometry and Mathematical Physics Seminar 2013/2014

Thursday 28 November 2013. The Frank Adams Room (Room 1.212), the Alan Turing Building. 3.15pm

Higher Poisson and Higher Koszul Brackets. II

Theodore Voronov (University of Manchester)

Continuation of the talk on November 14. (Last time I managed to introduce even and odd Poisson structures, their description in terms of bivector fields and odd quadratic Hamiltonians respectively and the explained role of the "master equation" $[P,P]=0$. A substantial part of the talk was devoted to a digression into the Gerstenhaber bracket and the Stasheff bracket, and the role of the Gerstenhaber bracket for describing associative products. Then we explained the construction of the binary Koszul bracket of differential forms on a Poisson manifold using the supermanifold language and the Mackenzie--Xu theorem.)

The central part of this talk is a discussion of $L_{\infty}$-algebras and, in particular, their description in terms of homological vector fields. The author's construction of higher derived brackets is presented in this special case. Next time there is a hope to move on to higher Koszul brackets as promised.