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Reiner I. — Representation theory of finite groups and related topics (Proceedings of symposia in pure mathematics)
Reiner I. — Representation theory of finite groups and related topics (Proceedings of symposia in pure mathematics)



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Название: Representation theory of finite groups and related topics (Proceedings of symposia in pure mathematics)

Автор: Reiner I.

Аннотация:

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.

A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

Read more at http://ebookee.org/A-Primer-on-Mapping-Class-Groups-PMS-49-Princeton-Mathematical_1558997.html#GfyXu5RwL2yS232W.99


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1971

Количество страниц: 185

Добавлена в каталог: 16.04.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$AG(d,q_{2})$      68
$a_{\chi}$ = $max\{|G|p/|B||B\in\mathscr{V}_{\chi}\}$      19
$M_{\mathfrak{D}(G)}$(M-homogeneous)      21 22
$M_{\mathscr{C}}$($\mathscr{C}_{1}$-free)      21 22
$N(\phi)$      20
$PSU_{4}(3)$      107
$\delta$-theorem      117
$\lambda$-ring      155
$\mathscr{C}$-decomposition      29
$\mathscr{C}$-decomposition, isomorphic refinements      30
1-1 condition      141
Abelian normal subgroup      37
Adams operations      156
Adjoints to restriction      42
Admissible lattice      169
Admissible lattice, irreducibility criterion      170
Admissible transformations      113
Affine group      146
Algebra      111
Algebra, bounded type      111
Algebra, finite type      111
Algebra, indecomposable representations      111
Algebra, matrix questions      113
Algebra, polynomial part      120
Algebra, strongly unbounded type      111
Algebra, unbounded type      111
Algebraic maps      39 40 42 43
Algebraic maps, transfer      42 44
Alternating form      73
Alternating group      95
Automorphism      25
Automorphism (B,N) pair      91
Basic set      8
Bass-order      130 137—142
Bass-order, completely primary      133
Bass-ring      131 137
Block, type of block      10
Bounded type      111
Brauer characters      124
Brauer homomorphism      140
Brauer's first fundamental theorem      141
Brauer's second fundamental theorem      142
Brauer's second main theorem on blocks      124
Cancellation      85
Cancellation for modules      31
Category of G-functors      42
Character ring functor      58
Character table      97
Characteristic powers      1
Characterization of characters      124
Characters      49 51
Characters, Brauer characters      124
Characters, character table      97
Characters, characterization of characters      124
Characters, extension of character      51
Characters, invariant      51
Characters, irreducible      3 80—82 146
Characters, orthogonality relations      49
Characters, permutation      73
Characters, principal indecomposable      123
Characters, q-modular (Brauer)      97
Chevalley groups      1
Chevalley groups, finite      13
Chevalley groups, Hecke algebra      2
Chevalley groups, irreducible representation      13 169
Cohomology ring functor      59
Completely primary Bass-order      133
Compounds      92
Conjugacy classes      51 78
Contravariant form      170
Conway group      108
Cusp form      150
Decomposition matrix      124
Decomposition numbers      138
Defect 0 and 1      142
Defect base      60
Defect group      61 139
Defect-basis      44
Doubly transitive group      67
Exchange property      30
Exponentials      40
Extension of character      51
F.C. subgroup      117
Factorizable groups      77
Fields of characteristic p      99
Finite Chevalley groups      13
Finite groups, $AG(d,q_{2})$      68
Finite groups, $N(\phi)$      20
Finite groups, $PSU_{4}(3)$      107
Finite groups, (B,N) pair      91
Finite groups, 1-1 condition      141
Finite groups, adjoints to restriction      42
Finite groups, algebraic maps      39 40 42 43
Finite groups, alternating group      95
Finite groups, automorphism      25
Finite groups, basic set      8
Finite groups, Brauer homomorphism      140
Finite groups, Chevalley groups      1
Finite groups, Conjugacy classes      51 78
Finite groups, Conway group      108
Finite groups, doubly transitive group      67
Finite groups, exponentials      40
Finite groups, fixed point subgroup      25
Finite groups, G-functor      42 43 44 57 124
Finite groups, generalized quaternion groups      74
Finite groups, GL(n,C)      37
Finite groups, Hecke algebra      91
Finite groups, hyperelementary groups      97
Finite groups, indecomposable representations      89
Finite groups, index parameters of G      91
Finite groups, integral representation ring      173
Finite groups, leech lattice      108
Finite groups, linear group      37
Finite groups, metacyclic groups      65 79
Finite groups, nonsimplicity      47
Finite groups, onto condition      141
Finite groups, permutation character      73
Finite groups, projective oG-modules      88
Finite groups, real representations      66
Finite groups, reflection representation      92
Finite groups, relative Grothendieck rings      44 99
Finite groups, representation modules      165 166
Finite groups, representations of finite groups      99
Finite groups, Suzuki group      107
Finite groups, sylow 2-subgroups of simple groups      53
Finite groups, units in $\Omega(G)$      41
Finite groups, X-graded Clifford system      20
Finite type      111
Fixed point subgroup      25
Frobenius algebra      49
Frobenius algebra, characters      49
Frobenius — Schur formula      98
Frobenius-Schur formula      98
Fundamental module      89
G-algebra      59
G-functor      42 43 44 57 124
G-functor, category of G-functors      42
G-functor, character ring functor      58
G-functor, cohomology ring functor      59
G-functor, defect base      60
G-functor, defect group      61 139
G-functor, G-algebra      59
G-functor, Grothendieck ring functors      59
G-functor, subgroup category      58
G-functor, transfer theorem      61
Genera of R-lattices      85
Generalized polynomial identity      119
Generalized quaterion groups      74
Generic degree      2
Generic ring      1 92
Genus      85
Genus, restricted genus      87
GL(n,C)      37
Gorenstein-ring      131—133 137 138
Green's polynomials      149
Grothendieck ring functors      59
Group ring      117
Group, Lie      13
Group, primitive      37
Group, simple      13 161
Hecke algebra      2 91
Hyperelementary groups      97
Indecomposable lattice      137 140
Indecomposable representations      89 111
Indecomposable representations, infinite type      111
Index parameters of G      91
Induction theorems      44 45
Infinite type      111
Integral representation      85
Integral representation ring      173
Invariant character      51
Invariant character, $\pi$-blocks      124
Invariant character, parabolic type      3
Irreducibility criterion      170
Irreducible character      3 80-82 146
Irreducible character, generic degree      2
Irreducible character, green's polynomials      149
Irreducible representation      13 169
Isomorphic refinements      30
Krull — Schmidt (— Azumaya) theorem      29
Lattice, cancellation      85
Lattice, genera of R-lattices      85
Lattice, genus      85
Lattice, indecomposable      137 140
Lattice, local direct factor of M      87
Leech lattice      108
Lie algebra Cusp form      150
Lie groups      13
Linear group      37
Local direct factor M      87
Matrix questions      113
Matrix questions, admissible transformations      113
Metacyclic groups      65 79
Metacyclic groups, split      65
Modular theory of permutation representations      137
Modules, $M_{\mathfrak{D}(G)}$(M-homogeneous)      21 22
Modules, $M_{\mathscr{C}}$($\mathscr{C}_{1}$-free)      21 22
Modules, $\mathscr{C}$-decomposition      29
Modules, admissible lattice      169
Modules, Brauer's first fundamental theorem      141
Modules, cancellation for modules      31
Modules, contravariant form      170
Modules, decomposition numbers      138
Modules, defect 0 and 1      142
Modules, exchange property      30
Modules, fundamental      89
Modules, Krull — Schmidt (— Azumaya) theorem      29
Modules, Schur index      97
Modules, tensor product theorem      171
Modules, vertex      165 166
Nilpotent radical      118
Nonsimplicity      47
O-order      85
Onto condition      141
Order, bass-order      130 137 142
Order, integral representation      85
Orthogonal idempotent decomposition      166 167
Orthogonality relations      49
Orthogonality relations, $\pi$-blocks      124
Orthogonality relations, Brauer's second main theorem on blocks      124
Parabolic type      3
Parabolic type, partially ordered set      114
Permutation character      73
Polynomial identity      118
Polynomial part      120
Prime rings      117
primitive      37
primitive      37
Principal indecomposable characters      123
Principal indecomposable characters      123
Projective ideal      166
Projective ideal      166
Projective ideal, orthogonal idempotent decomposition      166 167
Projective oG-modules      88
Projective oG-modules      88
q-modular (Brauer) character      97
Real representations      66
Real representations      66
Reflection representation      92
Reflection representation      92
Reflection representation, compounds      92
Reflection representation, compounds      92
Relative Grothendieck rings      44 99
Relative Grothendieck rings      44 99
Relative Grothendieck rings, Defect-basis      44
Relative Grothendieck rings, Defect-basis      44
Relative Grothendieck rings, induction theorems      44 45
Relative Grothendieck rings, induction theorems      44 45
Representation algebra      165
Representation algebra      165
Representation modules      65 66
Representation modules      65 66
Representation modules, projective ideal      166
Representation modules, representation algebra      165
Representation of finite groups      99
Representation of finite groups      99
Representation of finite groups, modular theory of permutation representations      137
Restricted genus      87
Restricted genus      87
Ring, $\Delta$-theorem      117
Ring, $\Delta$-theorem      117
Ring, $\lambda$-ring      155
Ring, $\lambda$-ring      155
Ring, Adams operations      156
Ring, Adams operations      156
Ring, bass-ring      131 137
Ring, bass-ring      131 137
Ring, Generalized polynomial identity      119
Ring, Gorenstein-ring      131—133 137 138
Ring, group ring      117
Ring, integral representation ring      173
Ring, integral representation ring      173
Ring, o-order      85
Ring, o-order      85
Ring, polynomial identity      118
Ring, polynomial identity      118
Ring, prime      117
Ring, prime      117
Ring, semiprime      118
Ring, semisimple      120
Ring, semisimple      120
Ring, splitting principle      155
Schur index      97
Schur index      97
Semiprime rings      118
Semiprime rings, nilpotent radical      118
Semisimple rings      120
Semisimple rings      120
Semisimple rings sets of primes      123
Semisimple rings sets of primes      123
Simple groups      13 162
Simple groups      13 162
Split metacyclic groups      65
Split metacyclic groups      65
Splitting principle      155
Splitting principle      155
Strongly embedded subgroup      69
Strongly embedded subgroup      69
Strongly unbounded type      111
Subgroup category      58
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