The calculus of multivectors on noncommutative jet spaces.
Arthemy Kiselev (Groningen)
What 


When 
Nov 30, 2017 from 03:30 pm to 04:30 pm 
Where  Mainz, 05432 (Hilbertraum) 
Add event to calendar 
vCal iCal 
Abstract.
The Leibniz rule for derivations is invariant under cyclic permutations of comultiples within the arguments of derivations. We explore the implications of this principle: in effect, we construct a class of noncommutative bundles in which the sheaves of algebras of walks along a tesselated affine manifold form the base, whereas the fibres are free associative algebras or, at a later stage, such algebras quotients over the linear relation of equivalence under cyclic shifts. The calculus of variations is developed on the infinite jet spaces over such noncommutative bundles.
In the frames of such fieldtheoretic extension of the Kontsevich formal noncommutative symplectic (super)geometry, we prove the main properties of the Batalin–Vilkovisky Laplacian and Schouten bracket. We show as byproduct that the structures which arise in the classical variational Poisson geometry of infinitedimensional integrable systems do actually not refer to the graded commutativity assumption.