×

zbMATH — the first resource for mathematics

Some aspects of the theory of quantum groups. (English. Russian original) Zbl 0839.17011
Russ. Math. Surv. 48, No. 6, 41-79 (1993); translation from Usp. Mat. Nauk 48, No. 6(294), 39-74 (1993).
This is a survey of some of the basic material on quantum groups. From the author’s introduction we quote: “We do not set ourselves the goal of surveying all the various theoretical and applied aspects of quantum groups, but prefer to take one example – multiparameter deformation of the group \(GL_n\) – in more or less detail, stating and partially proving some general results on the way. Thus we hope to reproduce a significant part of the theory of quantum groups which is useful for a first acquaintance with the subject.”
The main topics treated are: Basic definitions in Hopf algebra theory, \(R\)-matrix algebras, representations of quantum groups, quantum flag spaces, Schur algebras, the Frobenius morphism, noncommutative differential calculus, quantum Weyl algebras.

MSC:
17B37 Quantum groups (quantized enveloping algebras) and related deformations
17-02 Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
46L85 Noncommutative topology
46L87 Noncommutative differential geometry
PDF BibTeX XML Cite
Full Text: DOI