ENGLISH

Topics in noncommutative geometry

By Yuri I. Manin

Book information

Publisher
Princeton University Press
Year
1991
ISBN
0691085889, 9780691085883
LCC
QA564 .M36 1991
Open Library ID
OL1886039M
Language
english
Format
DJVU
Filesize
2 MB (1640678 bytes)
Pages
171\171
Library
kolxoz
DPI
200
Scanned
yes
Time added
2009-07-20 03:45:11

Description

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.

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