Rosenberg A.L. — Noncommutative Algebraic Geometry And Representations Of Quantized Algebras :: Электронная библиотека попечительского совета мехмата МГУ

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Rosenberg A.L. — Noncommutative Algebraic Geometry And Representations Of Quantized Algebras

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Название: Noncommutative Algebraic Geometry And Representations Of Quantized Algebras

Автор: Rosenberg A.L.

Аннотация:

This book contains an introduction to the recently developed spectral theory of associative rings and Abelian categories, and its applications to the study of irreducible representations of classes of algebras which play an important part in modern mathematical physics. Audience: A self-contained volume for researchers and graduate students interested in new geometric ideas in algebra, and in the spectral theory of noncommutative rings, currently invading mathematical physics. Valuable reading for mathematicians working on representation theory, quantum groups and related topics, noncommutative algebra, algebraic geometry, and algebraic K-theory.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1995

Количество страниц: 313

Добавлена в каталог: 02.12.2009

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Предметный указатель

$\omega$ -sheaves      I.6.3
$\vartheta$ -invariant primes      II.3.2.6
Adjoint hyperbolic category      IV.5.6
Adjoint hyperbolic ring      II.3.1.9
Affine schemes      1.7.0.4
Associated points      III.8 VI.1.6 VI.2.7
Blow up      VII.4.4
Bundle of localizations      1.7.0.1
Canonical anti-automorphism      II.3.1.8
Category of Heisenberg type      IV.7.3
Category of Weyl type      IV.7.7
Central topology      III.7.1
Characters      V.C2.5
Clifford type rings      IV.7.8
Complete spectrum      VI.1
Complete support      VI.1.5
Completely prime ideals      I.1.6
Conormal bundle      VII.4.1
Coordinate algebra of $SL_{q}(2)$       II.3.1.5
Coresidue categories      V.C3.3
Direct image functor      VII.1.3
Essential length      V.C2.1
Exact localizations      III.2.1
Flat localizations      1.0.4
Flat spectrum      VI.2
Flat support      VI.2.6
Formal neighborhood of a topologizing subcategory      VII.4.3
Gabriel functor      I.0.4
Gabriel multiplication      I.0.2 VI.1.3.3
Gabriel — Krull dimension      VI.6.0
Generating function      II.3.2.4
Global section functor      VII.1.5
Goldie rings      1.6.4
Goldman's spectrum      VI.3
Graded monads      V.4.1
Grading associated to a point of the spectrum      V.4.3
Grothendieck category      III.3.0
Hyperbolic category      IV.5
Hyperbolic ring      II.intr. II.3.1.4
Hyperbolic ring associated to a Kac-Moody Lie algebra      V.C5.1
Indecomposable injective spectrum      VI.5.1
Injective spectrum      VI.5.1
Inverse image functor      VII.1.1
Iterated hyperbolic category      IV.6.12.2
Iterated hyperbolic ring      IV.6.12.3
Kac — Moody Lie algebras      V.2.5
L-Systems      I.4.1
Left normal morphisms      1.3.2
Left normal rings      I.3.2.2
Left projective spectrum      I.7.2.2
Left radical      I.4.0
Left spectrum      I.1.5
Levitzki radical      I.4.4
Levitzki spectrum      I.5.1
Local algebra setting      I.7.0.4
Local algebra setting for quasi-affine schemes      I.7.1.4
Local categories      III.2.4

Localizations at points      III.2.6
Locally associated points      V.C2.3
Locally finite objects      V.C2.2
Locally nilpotent ring      I.4.4
Locally noetherian categories      VI.6.0.5
Monad associated with $(\theta, \xi)$       IV.5.3
Morphisms (co)flat      VII.1.3
Morphisms affine      VII.1.4
Morphisms continuous      VII.1.3
Morphisms quasi-affine      VII.1.3
Multiplicative system      I.0.3.1
Nil-ring, nil-ideal      I.4.7
Open embeddings      I.7.0.3
PBW monad      V.2.3
PBW rings      V.2.4
Prime spectrum      I.1.7
Prime spectrum of a category      III.C1
Principal ideal domain      I.C1
Projective spectrum      VII.2.6
Quantum coordinate algebra of SL(2)      II.3.1.5
Quantum enveloping algebra of sl(2)      II.3.1.2
Quantum plane      I.C2
Quantum Weyl algebra      II.C2.8 V.C4.5
Quasi-affine schemes      I.7.1
Quasi-cofinite objects      V.C3.5
Quasi-coherent presheaves      I.6.0
Quasi-holonomic modules      V.C2.1
Quasi-schemes      VI.7 VII.1.2
Quotient category      I.0.4
Radical filters      I.0.3
Reduction modulo N      IV.6.9
Restricted skew polynomial ring      II.2.1
Ring of Heisenberg type      IV.7.1
Serre subcategories      III.2.3.2
Skew affine space      VII.2.4.2
Skew Laurent category      IV.2
Skew Laurent polynomials      II.1.2
Skew PBW comonads      V.C3.6
Skew polynomial category      IV.1
Skew polynomials      II.1
Skew projective space      VII.2.4.3
Sober space      I.5.2
Spectrum of a category      III.1.2
Subcategory of skew double points      IV.1.3
Support      I.1.11 III.5.2
Symmetric monad      VII.3.2
Tautological exact sequence      VII.3.6
The exterior monad      VII.3.3
Thick subcategories      III.2.1
Topology $\tau$       III.5.1
Two-parameter deformations of M(2) and GL(2)      V.C6
Uniform subcategories      VI.1.3
Universal hyperplane sheaf      VII.3.6
Upper nil-radical = Kethe radical      1.4.7.1
Verma functor      IV.5.8
Veronese submonad      VII.2.10.1
Virasoro algebra      V.2.7
Zariski topology      I.10.2 III.6.9

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