(Ebook) Invariant Differential Operators. Volume 2: Quantum Groups by Vladimir K. Dobrev ISBN 9783110435436, 9783110427707, 3110435438, 3110427702

(Ebook) Invariant Differential Operators. Volume 2: Quantum Groups by Vladimir K. Dobrev ISBN 9783110435436, 9783110427707, 3110435438, 3110427702

Main subject categories: • Group theory and generalizations • Rings and algebras • Quantum Theory • Mathematical Physics • and more[From the preface]This is volume 2 of our set on invariant differential operators. In volume 1 we presented our canonical procedure for the construction of invariant differential operators and showed its application to the objects of the initial domain – noncompact semisimple Lie algebras and groups.In volume 2 we show the application of our procedure to quantum groups. Similarly to the setting of volume 1 the main actors are in duality. Just as Lie algebras and Lie groups are in duality here the dual objects are the main two manifestations of quantum groups: quantum algebras and matrix quantum groups. Actually, quantum algebras typically are deformations of the universal enveloping algebras of semisimple Lie algebras. Analogously, matrix quantum groups typically are deformations of spaces of functions over semisimple Lie groups.