In this survey article we describe some geometric results in the theory of noncommutative
rings and, more generally, in the theory of abelian categories. Roughly speaking and by …

Our geometric concepts evolved first through the discovery of Non-Euclidean geometry. The
discovery of quantum mechanics in the form of the noncommuting coordinates on the phase …

Categories enriched with tensor products, here called tensor categories, but also called
monoidal categories, have been studied and used extensively in the literature [ML1, EK …

This invaluable book is an introduction to knot and link invariants as generalised amplitudes
for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical …

The goal of this first paper is to formalise the use of certain diagrams for a wide variety of
situations in pure and applied mathematics. The main examples are the Feynman diagrams …

A new realisation of the quantum group SU q (2) is constructed by means of a q-analogue to
the Jordan-Schwinger mapping, determining thereby both the complete representation …

Standard (Drinfeld-Jimbo) q-deformation of the Cartan-Weyl basis for o (3, 2)(real form of
B2)⋍ sp (4| R)(real form of C2) is calculated. The limit R→∞(R is the anti-de Sitter radius) …

We first exhibit in the commutative case the simple algebraic relations between the algebra
of functions on a manifold and its infinitesimal length element ds. Its unitary representations …

This is an introduction to non-commutative geometry, with special emphasis on those cases
where the structure algebra, which defines the geometry, is an algebra of matrices over the …

This book introduces recent developments in the study of algebras defined by quadratic
relations. One of the main problems in the study of these (and similarly defined) algebras is …