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Street R., Murray M. (Ed), Broadbridge Ph. (Ed) — Quantum Groups: A Path to Current Algebra
Street R., Murray M. (Ed), Broadbridge Ph. (Ed) — Quantum Groups: A Path to Current Algebra



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Название: Quantum Groups: A Path to Current Algebra

Авторы: Street R., Murray M. (Ed), Broadbridge Ph. (Ed)

Аннотация:

Algebra has moved well beyond the topics discussed in standard undergraduate texts on 'modern algebra'. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn the latest algebraic concepts and techniques. A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an 'algebra'. Another part is not in those standard books at all: a comultiplication, which is dual to multiplication in the precise sense of category theory, making it a 'coalgebra'. While coalgebras, bialgebras and Hopf algebras have been around for half a century, the term 'quantum group', along with revolutionary new examples, was launched by Drinfel'd in 1986.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 260

Добавлена в каталог: 23.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
2-category      100 102
2-cell      97
2-cell, 2-category      100
2-cell, 2-functor      101 102
2-cell, identity      98
2-cell, pasting      97
2-functor      101 102
A-module      101
A-module action      101
A-module arrow      101
A-module, left      101
A-point      55
action      59 101 111
Action of an A-module      101
Adjoining an antipode      117
Adjoining an inverse for the determinant      56
Adjoining, left-dual objects      117
Adjoint, left      111
Adjoint, left 2-adjoint      111
Adjoint, Lie algebra      33
Algebra, exterior      31
Algebra, Hopf      51
Algebra, morphism      27
Algebra, of endomorphisms      28
Algebra, of formal power series      42
Algebra, opposite      30
Algebra, over R      21
Algebra, polynomial algebra      45
Algebra, polynomial R-algebra      46
Algebra, R-algebra      27
Algebra, symmetric      45
Algebra, tensor      28
Algebra, universal      87
Algebra, universal enveloping      40
Algebraic geometry      5
Algebraic varieties      5
Antipode      7 51 105 117
Appropriate representation      11)3
Arrow between monoid arrows      97
Arrow composition      78
Arrow monoid      97
Arrow of category      6
Associativity      2 27 67
Autonomous      82
Autonomous, left      81
Autonomous, left/right      82
Balanced      106
Balanced bialgebra      76
Balanced YB-operator      88
Banach spaces      79
Banach spaces, example of closed symmetric tensor category      79
Bialgebra, balanced      76
Bialgebra, braided      72
Bialgebra, commutative over k      7
Bialgebra, matrix bialgcbra      46
Bialgebra, morphia in      44
Bialgebra, quasitriangular      72
Bialgebra, R-bialgebra      42
Bialgebra, symmetric      72
Bialgebra, triangular      72
Biclosed      78
Bilinear, R-bilinear      15
Bilinear, universal bilinear function      15
Bimodule, left R-fright s-bimodule      16
Bimonoid      105
Bimonoid in $Mod_R$      105
Bimonoid in V      105
Bimonoid with a braiding      106
Bimonoid with a twist      106
Bimonoid, balanced      106
Bimonoid, cobalanced      108
Bimonoid, cobraided      108
Bimonoid, cotortile      108
Bimonoid, strict quasi-bimonoid      105
Bimonoid, tortile      108 114
Bisection, canonical      1
Bradshaws      xvii
Bradshaws, Age of String      xviii
Bradshaws, Bradshaw Foundation      xvii
Bradshaws, Edition Limitee      xvii
Bradshaws, Grahame Walsh      xvii
Bradshaws, silhouette      viii 8 20 26 36 46 58 66 92 116 118 132 141
Braid category      69
Braid composition      69
Braid group, of Artin      69
Braid, tensor product      69
Braided      114
Braided bialgebra      72
Braided tensor category      68
Braiding      68 83 105
Braiding element      72
Braiding for a bimonoid      105
Braiding for a tensor category      68
Brown, Ronald      xviii
Byrne, Simon      xvi
C*-algebra, commutative      5
Cartan, Eli      33
Cartesian product      x 1
Cartesian product of no sets      1
Category      xi
Category of braids      69
Category, dual      xii
Category, functor category      xiv
Category, functors      xiii
Category, monoidal      67
Category, morphisms      xi
Category, objects      xi
Category, of monoids in V      100
Category, opposite      xii
Category, strict, tensor      104
Category, tensor      67
Cauchy H-comoduIe      65
Cauchy moduler      21
Closed functor      86
Closed tensor category      78
Closed, left-closed      77
Co-element, co-T-elements      x
Coaction      62
Coalgebra over a ring      37
Coalgebra, morphism      38
Coalgebra, primitive element      41
Coalgebra, set-like element      40
Cobraiding      108
CoCauchy      47
Cocommutative coalgebra      38
Codomain target      xii
Coend      115
Coherence theorem of Mac Lane      68 109
Commutative      3 30
Commutative Lie algebra      35
Commutative monoid      3
Commutative R-algebra      30
Commutative rig      4
Commutativity      3
Commutator defines a Lie bracket      32
Commute with diagonals      45
Comodule      59 62
Comodule morphism      62
Comodule, left      62
Composable morphisms      xii
Composite morphism      xii
Composite, pasted      100
Composition arrow      78
Composition of braids      69
Composition, vertical      98
Comuttiplication      7- 8 37
Constraint, associativity      67
Constraint, left unit      67
Constraint, right unit      67
Convergent      24
Convolution product      39
Convolution structure      38
Coordinate algebra      9
Coordinate algebra, quantum matrices      0
Coordinate k-algebra      8
Coordinate k-algebra of general linear group      8
Coproduct      xiii
Coprojection      8
Coset      14
Coset, H-coset      14
Coterminal object      xiii
Cotwist      108
Counit      7 37 81
Cramer Rule quantum      120
Derivation      32
Diagonal      1
Diagonal in category X      7
Diagonal, formal      37
Diagonal, ternary      1
Direct sum of Lie algebras      34
Direct sum of modules      24
Disjoint union, X +Y      x
Distributive      4
Domain source      xii
Drinfel'd, Vladimir G.      105
Drinfel'd, Vladimir G., International Congress of Mathematicians, 1986      ix
Dual      21
Dual category      xii
Dual, left dual      21
Dual, opposite      xii
Dual, right dual      81
Duality principle      x
Dualizing object      80
Dualizing object, left      79
Dualizing object, right      80
END      109 110
End is a limit      113
Endomorphism algebra      28
enrich      18
Enrich, abelian group with module structure      18
Equalizer      109
Essentially      104
Evaluation      77
Evaluation functor      95
Evaluation morphism      19
Exponential series      30
Exterior algebra      31
Faddc'ev, Ludwig D.      10
Field      4
Finitely generated      13
Forgetful functor      31 101 115
Formal diagonal      37
Formal power series      42
Formal Tannaka Duality      111
free      14
Free constructions      31
Free module      14
Free module from R to S, generated by X      16
Free module, functor      86
Freyd, Peter      82
Function identity      1
Function, complex-valued      5
Function, continuous      5
Function, diagonal      1
functor      xiii
Functor category      xiv
Functor, essentially weak tensor      103
Functor, evaluation      95
Functor, forgetful      101
Functor, natural transformation      xiv
Functor, represent able      xiv
Functor, represented by T      xiii
Functor, self-adjoint      54
Functor, tensor      85
Functor, weak tensor functor      101
Fundamental theorem on coalgebras      115
Funny superscripts      10
Gelfand duality      5
General linear group      8
General linear group, commutative Hopf algebra      8
General linear group, coordinate k-algebra      8
Generalised co-element      x
Generate      13
Generic point      10
Geometric series      28
Grassmannian algebra      10
Group      2 7
Group, affine over k      7
Group, diagrammatic definition      7
Group, Lie group      7
Group, R-algebra      29
Group, topological group      7
Homomorphism, generalised co-element      x
Homothety      96
Hopf algebra      7 51
Hopf algebra, commutative      7 53
Hopf monoid      113
Hopf monoid, quasi      105
Hurwitz polynomials      45
Ideal      29
Ideal in an algebra      29
Identity      1 2 27 84
Identity morphism      xii
Identity, 2-cell      98
Incidence, projective plane      xi
Indeterminate      42
Initial object      xiii
Injective      24
Injective morphism      24
Internal horn      77 110
Internal horn, left      77
Internal horn, right      78
Inverse, left- and right-inverses agree      xiii
Invertibility      2
Invertible      2
Invertible isomorphism      xiii
Invertible morphism      xiii
Isomorphic      xiii
Isomorphism      xiii. 4
Isomorphism, invertible      xiii
Isomorphism, isomorphic      xiii
Isomorphism, natural      xiv
Jacobi identity      32
Joyal, Andre      xvi 91 117
k-algebra      4
k-algebra, coordinate algebra      8
k-algebra, morphism      4
Katis, Piergiulio      117
Kobyzev, Yu.      10
Kronecker delta      57
Left 2-adjoint      111
Left adjoint      111
Left dual      81
Left dual as a functor      81
Left dual of a module      21
Left dual of a signed set      83
Left inverse      xiii
Left R-linear      14
Left-closed      77
Leibniz rule      32
Lie algebra      32 33
Lie algebra, adjoint      33
Lie algebra, commutative      35
Lie algebra, direct sum      34
Lie algebra, Lie bracket      32
Lie algebra, morphism      33
Lie algebra, universal enveloping      33
Lie bracket      32 33
Lie group      33
Lie. Sophus      33
1 2
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