A new family of algebraic operations, the k-divergences, generalizes the Turaev cobracket and, for free associative algebras, coincides with ribbon graph operations and the standard cohomology generators of gl_n.
Lectures on Noncommutative Geometry
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These Lectures are based on a course on noncommutative geometry given by the author in 2003 at the University of Chicago. The lectures contain some standard material, such as Poisson and Gerstenhaber algebras, deformations, Hochschild cohomology, Serre functors, etc. We also discuss many less known as well as some new results, in particular, noncommutative Chern-Weil theory, noncommutative symplectic geometry, noncommutative differential forms and double-tangent bundles.
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A family of algebraic operations extending the Turaev cobracket
A new family of algebraic operations, the k-divergences, generalizes the Turaev cobracket and, for free associative algebras, coincides with ribbon graph operations and the standard cohomology generators of gl_n.