---

＜E-Book＞
Noncommutative Algebraic Geometry and Representations of Quantized Algebras / by A. Rosenberg
(Mathematics and Its Applications ; 330)

Edition	1st ed. 1995.
Publisher	(Dordrecht : Springer Netherlands : Imprint: Springer)
Year	1995
Language	English
Size	XII, 322 p : online resource
Authors	*Rosenberg, A author SpringerLink (Online service)
Subjects	LCSH:Associative rings LCSH:Associative algebras LCSH:Topological groups LCSH:Lie groups LCSH:Algebra, Homological LCSH:Mathematics FREE:Associative Rings and Algebras FREE:Topological Groups and Lie Groups FREE:Category Theory, Homological Algebra FREE:Applications of Mathematics
Notes	I Noncommutative affine schemes -- II The left spectrum and irreducible representations of ‘small’ quantized and classical rings -- III Noncommutative local algebra -- IV Noncommutative local algebra and representations of certain rings of mathematical physics -- V Skew PBW monads and representations -- VI Six spectra and two dimensions of an abelian category -- VII Noncommutative Projective Spectrum -- Reference -- Index of Notations This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It is helpful, however, to know some basics of algebraic geometry and representation theory. Each chapter begins with its own introduction, and most sections even have a short overview. The purpose of what follows is to explain the spirit of the book and how different parts are linked together without entering into details. The point of departure is the notion of the left spectrum of an associative ring, and the first natural steps of general theory of noncommutative affine, quasi-affine, and projective schemes. This material is presented in Chapter I. Further developments originated from the requirements of several important examples I tried to understand, to begin with the first Weyl algebra and the quantum plane. The book reflects these developments as I worked them out in reallife and in my lectures. In Chapter 11, we study the left spectrum and irreducible representations of a whole lot of rings which are of interest for modern mathematical physics. The dasses of rings we consider indude as special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra ofthe Lie algebra sl(2) , coordinate algebra of the quantum group SL(2), the twisted SL(2) of Woronowicz, so called dispin algebra and many others HTTP:URL=https://doi.org/10.1007/978-94-015-8430-2

 Similar Items