"There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off the de Rham complex; and so on. In this book Yuri Manin addresses a variety of instances in which the application of commutative algebra cannot be used to describe geometric objects, emphasizing the recent upsurge of activity in studying noncommutative rings as if they were function rings on ""noncommutative spaces."" Manin begins by summarizing and giving examples of some of the ideas that led to the new concepts of noncommutative geometry, such as Connes' noncommutative de Rham complex, supergeometry, and quantum groups. He then discusses supersymmetric algebraic curves that arose in connection with superstring theory; examines superhomogeneous spaces, their Schubert cells, and superanalogues of Weyl groups; and provides an introduction to quantum groups. This book is intended for mathematicians and physicists with some background in Lie groups and complex geometry. Originally published in 1991.
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905."
By:
Yuri I. Manin
Imprint: Princeton University Press
Country of Publication: United States
Volume: 16
Dimensions:
Height: 254mm,
Width: 178mm,
Spine: 11mm
Weight: 510g
ISBN: 9780691635781
ISBN 10: 0691635781
Series: Princeton Legacy Library
Pages: 174
Publication Date: 28 June 2016
Audience:
College/higher education
,
Professional and scholarly
,
Primary
,
Undergraduate
Format: Hardback
Publisher's Status: Active
*FrontMatter, pg. i*CONTENTS, pg. v*PREFACE, pg. vii*CHAPTER 1 . AN OVERVIEW, pg. 3*CHAPTER 2. SUPERSYMMETRIC ALGEBRAIC CURVES, pg. 33*CHAPTER 3. FLAG SUPERSPACES AND SCHUBERT SUPERCELLS, pg. 96*CHAPTER 4. QUANTUM GROUPS AS SYMMETRIES OF, pg. 124*BIBLIOGRAPHY, pg. 157*INDEX, pg. 164
Reviews for Topics in Non-Commutative Geometry
"""[This reviewer] like[s] the book a lot. First, because of the excellent mathematics it contains. But second, because of the truly enlightening way this mathematics gets conveyed to the reader.""--Bulletin of the American Mathematical Society"
