This paper stands at the interface between combinatorial Hopf algebra theory and
renormalization theory. Its plan is as follows: Sec. 1.1 is the introduction, and contains an …

This volume attempts to give a comprehensive discussion of the theory of operator algebras
(C*-algebras and von Neumann algebras.) The volume is intended to serve two purposes: to …

We develop a geometric approach to A-infinity algebras and A-infinity categories based on
the notion of formal scheme in the category of graded vector spaces. The geometric …

N oncommutative geometry, in the sense in which this book uses the term, is to a very large
extent the creation of a single mathematician, Alain Connes. Chapter 3, indeed, begins with …

We develop geometric approach to A-infinity algebras and A-infinity categories based on the
notion of formal scheme in the category of graded vector spaces. Geometric approach …

A bstract We explore a class of CFT's with higher spin currents and charges. Away from the
free or N=∞ limit the non-conservation of currents is governed by operators built out of the …

Let M be any compact simply-connected oriented d-dimensional smooth manifold and let F
be any field. We show that the Gerstenhaber algebra structure on the Hochschild …

Abstract The Split Field Magnet facility at the CERN ISR has been used to measure inclusive
resonance production in inelastic pp collisions at a cm energy of 53 GeV. The mass …

Proofs of Tsygan's formality conjectures for chains would unlock important algebraic tools
which might lead to new generalizations of the Atiyah-Patodi-Singer index theorem and the …

We first review various known algebraic structures on the Hochschild (co) homology of a
differential graded algebras under weak Poincar {\'e} duality hypothesis, such as Calabi-Yau …