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Noncommutative Algebraic Geometry and Representations of Quantized Algebras (Paperback, Softcover reprint of hardcover 1st ed. 1995)
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Noncommutative Algebraic Geometry and Representations of Quantized Algebras (Paperback, Softcover reprint of hardcover 1st ed. 1995)
Series: Mathematics and Its Applications, 330
Expected to ship within 10 - 15 working days
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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.
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