We review the present status of gauge theories built on various quantum space–times
described by noncommutative space–times. The mathematical tools and notions underlying …

This is the first extensive treatment of the theory of corings and their comodules. In the first
part, the module-theoretic aspects of coalgebras over commutative rings are described …

This is an introduction for algebraists to the theory of algebras and Hopf algebras in braided
categories. Such objects generalise super-algebras and super-Hopf algebras, as well as …

This book provides a self-contained introduction to quantum groups as algebraic objects.
Based on the author's lecture notes for the Part III pure mathematics course at Cambridge …

We continue studies on quantum field theories on noncommutative geometric spaces,
focusing on classes of noncommutative geometries which imply ultraviolet and infrared …

In the past decade there has been an extemely rapid growth in the interest and development
of quantum group theory. This book provides students and researchers with a practical …

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 define a new homotopy algebraic structure, that we call a braided L_ ∞ L∞-algebra,
and use it to systematically construct a new class of noncommutative field theories, that we …

A gauge invariant notion of a strong connection is presented and characterized. It is then
used to justify the way in which a global curvature form is defined. Strong connections are …

We develop a generalised theory of bundles and connections on them in which the role of
gauge group is played by a coalgebra and the role of principal bundle by an algebra. The …