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Noncommutative Poisson structures, Hochschild type complexes and Groebner bases theory

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Speaker: 
Natalya Iyudu
Affiliation: 
The University of Edinburgh/MPIM
Date: 
Tue, 2019-12-10 14:00 - 15:00
Location: 
MPIM Lecture Hall
We formulate the notion of pre-Calabi-Yau structure via the higher cyclic Hochschild complex and study its cohomology.
A small quasi-isomorphic subcomplex in higher cyclic Hochschild complex gives rise to the graphical calculus of $\xi\partial$-monomials.
Within this calculus   we are able to give a nice combinatorial  formulation of the Lie structure on the corresponding Lie subalgebra.

Then using  basis of  $\xi\partial$-monomials and employing elements of Groebner bases theory we prove homological purity of the
higher cyclic Hochschild complex and as a consequence obtain $L_\infty$-formality. This is based on a joint work with M. Kontsevich.

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