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Manin Yu.I. — Topics in noncommutative geometry
Manin Yu.I. — Topics in noncommutative geometry

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Название: Topics in noncommutative geometry

Автор: Manin Yu.I.

Аннотация:

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.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 163

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Associativity constraint      I.4.2
Bialgebra      I.3.2
Bott — Samelson superschemes      III.5.2
Braid group      I.3.6
Classical supergroups      III.1.1
Coalgebra      I.3.2
Commutativity constraint      I.4.2
Comodule      I.3.4
Connes's chain      I.2.13
Connes's cobordism      I.2.13
Connes's connection      I.2.14
Connes's cycle      I.2.1
Contact algebra      III.5.9
Cyclic complex      I.2.7
Cyclic object      I.2.6
Flag spaces      III.1.2
Flag Weyl group      III.1.6
Format of a multiplicative matrix      IV.1.1
Fredholm module      I.2.3
Frobenius algebra      IV.4.6
General linear supergroup      IV.3.1
Hochschild complex      I.2.9
Hopf algebra      1.3.2
Hopf algebra, superalgebra      IV.1.1
Hopf envelope      IV.1.4
Identity constraint      I.4.2
Integral in a Hopf algebra      IV.2.12
Lobachevsky's superptane      II.1.14
Monoidal category      I.4.2
Multiplicative matrix      I.3.4; I.3.5; IV.1.1
Neveu-Schwarz superalgebra      II.5.9
Noncommutative de Rham complex      I.2.4
Parabolic subgroups of supergroups      III.6.1
Pseudoabelian Lie superalgebra      II.7.1
Pseudodifferential operators      II.5.2; II.5.3
Pseudoinvariant of a triple      II.2.12
Quantum Berezinian      IV.3.8
Quantum group      I.3.3
Quantum space      IV.2.1
Quasi-Hopf algebra      I.4.4
Quasibialgebra      I.4.4
Quasitriangular Hopf algebra      I.4.4
Regular algebra, regular quantum space      IV.4.1
Relative cyclic homology      I.2.10
Riemannian supersphere      II.1.8
Schottky group      II.2.9
Schottky superdomain      II.2.13
Schottky unifonnization      II.2.9
Schubert supercells      III.2.2
Structure distributions      II.1.9
Supercross ratio      II.1.8
Superdiagonal      II.6.2 II.6.3
Superexponential function      II.8.1
Superlength in flag Weyl groups      II.3.2
Superprojective structure      II.4.1
Superresidue      II.6.4
Supertheta-function      II.8.3 II.8.4
Supertransposition      II.1.2 IV.1.1
SUSY-family      II.2.1
SUSY-structure      II.1.10
Tensor category      I.4.2
Theta-characteristic      II.2.2
Triangular Hopf algebra      I.4.3
Virasoro algebra      II.5.1
Yang — Baxter equations      I.3.6
Yang — Baxter equations, classical      I.3.7
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