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Gabriel P., Roiter A.V., Kostrikin A.I. (ed.) — Encyclopaedia of Mathematical Sciences. Volume 73: algebra VIII
Gabriel P., Roiter A.V., Kostrikin A.I. (ed.) — Encyclopaedia of Mathematical Sciences. Volume 73: algebra VIII

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Название: Encyclopaedia of Mathematical Sciences. Volume 73: algebra VIII

Авторы: Gabriel P., Roiter A.V., Kostrikin A.I. (ed.)

Аннотация:

This monograph aims at a general outline of old and new results on representations of finite-dimensional algebras. In a theory which developed rapidly during the last two decades, the lack of textbooks is the main impediment for novices. We therefore paid special attention to the foundations and included proofs for statements which are elementary, serve comprehension or are scarcely available. In this manner we try to lead the reader up to a point where he can find his way in the original literature.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 183

Добавлена в каталог: 04.04.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(\Box+\circ,[1\ 1])$      46
$(\Box,[1])$      46
$(\Box,\vdash\dashv)$      46
$(\varnothing, I)$      46
$/\Box$      157
$A_{\Box}$      57
$d_{\Box}$      103
$Ext(\Box, \circ)$      18
$E_{6}$, $E_{7}$, $E_{8}$      57
$GL_{\Box}$      4
$G_{\Box}$, $G_{\overline{\Box}}$, $G_{\Box\Box}$      8 65
$H(\Box)$      147
$Hom(\Box, \circ)$      16
$h\Box$      17
$H_{\Box}$      141
$Is\Box$      23
$J_{\Box}$      10
$k(\Box)$      144
$k[\Box]$      74
$k\Box$      16 17
$k^{2}\Box$      81
$k^{\Box\times\circ}$      4
$k^{\circ}(\Box)$      148
$k^{\circ}_{\mathscr{N}}(\Box)$      152
$K_{0}\Box$      134
$k_{\Box}$      31
$k_{\tau}\Box$      105
$mod^{\vee}\Box$      85
$mod_{f}\Box$      25
$mod_{pf}\Box$      29
$M^{\Box}$      34
$N^{\Box}$      44
$N_{\Box}$      121
$per_{0}\Box$      123
$per_{t}\Box$      123 124
$q(\Box|\circ)$, $q^{\Box}$, $q_{\Box}$      56
$q^{\Box}$      57
$q_{\Box}$      52 62
$R^{re}_{\Box}$, $R^{im}_{\Box}$      66 67
$sp\Box$      29
$t\Box$      17
$T_{\Box\Box}$      121
$U^{\otimes}$      125
$w(\Box)$      45
$W_{\Box}$      60 66
$X_{\Box}$      65
$[\Box,\circ[..$      101
$[\Box32,\circ]$      32
$\bigoplus\Box$      18
$\Box {}^{\times}_{\times} \circ$      47
$\Box/\circ$      16
$\Box\oplus\circ$      21
$\Box^{ {}^{\times}_{\times} }(\circ)$      47
$\Box^{*}$      21 43
$\Box^{-}$, $^{-}\Box$      31
$\Box^{-}(\circ)$, $\Box^{+}(\circ)$      47
$\Box^{k}$      34
$\Box^{k}_{\circ}$      35
$\Box^{l}$      8
$\Box^{\cdot}$, $\Box_{\cdot}$      159
$\Box^{\vee}$      31
$\Box^{\wedge}$      19
$\Box_{a}$      17
$\Box_{v}$      17
$\check{k}$      31
$\chi_{\Box}$      17
$\coprod$      33
$\coprod_{\Box}$      19
$\delta^{\Box}$      58 67
$\Gamma_{\Box}$      101 122—124
$\mathds{P}_{\Box}$      17
$\mathds{Z}\Box$      133
$\mathscr{A}(\Box,\circ)$      16
$\mathscr{C}(\Box)$, $\mathscr{C}_{\Box}$      42
$\mathscr{C}\Box$      130
$\mathscr{D}_{\Box}$      131
$\mathscr{F}_{\Box}$      154
$\mathscr{H}\Box$      130
$\mathscr{H}_{+}\Box$, $\mathscr{H}_{-}\Box$      131
$\mathscr{H}_{b}\Box$      131
$\mathscr{I}_{\Box}$      24
$\mathscr{P}_{\Box}$      144
$\mathscr{R}\Box$, $\mathscr{R}_{\Box}$      26
$\mathscr{R}^{\infty}_{\Box}$      74
$\mathscr{St}\Box$, $\mathscr{St}^{*}\Box$      54
$\mathscr{S}_{\Box}$      107
$\mathscr{T}$      82
$\omega$      16
$\overline{\Box}$      7 18
$\overrightarrow{\Box}$      143
$\Pi_{\Box}$      107
$\prod_{\Box}$      19
$\sigma_{\Box}$      60 105
$\tau$, $\overline{\tau}$      94 102
$\underline{dim}$      see "Dimension-function"
$\underline{\Box}$      89
$\varphi$      127
$\widehat{\Box}$      36 48
$\widetilde{A}_{\Box}$      58
$\widetilde{D}_{\Box}$      58
$\widetilde{E}_{6}$, $\widetilde{E}_{7}$, $\widetilde{E}_{8}$      58
$\widetilde{\Box}$      157
$^{l}\mathds{M}$, $\mathds{M}^{l}$, $^{l}\mathds{M}^{l}$      4
${\Box}^{'}_{\circ}$      47
$|\Box$      17
Abelian category      88
Additive category      21
Additive function      103
Additive hull      22
Admissible ideal      81
Affect      42
Aggregate      29
Algebra of a k-category, of a quiver      19
Almost split sequence      91
Annihilator of a module      45
Antichain      15
Arboresque      108
arrow      17
Artinian algebra      33
Avoid (space avoiding submodules)      34
Basis (of a module over a category)      43
Bigraph      56
Biinvolutive poset      43
Bimodule      15 88
c, C, $\overline{C}$      127 131
Canonical class      147
Category ($\neq$ k-category) of paths      17
Chain (poset)      15
Cleaving      146
Closed under extensions ...      100
Closed under extensions path      102
Coherent (module, spectroid)      85
Cohomology group of a ray-category      147
Complete component      104
Conflation      89
contour      145
Convex subcategory      159
Cotranslate      91
Cover, covering      157
Critical arboresque spectroid      108
Critical form      57
Critical path      149
Critical ray-category      162
Cross-section      8
Cyclic      45
D      31
Deflation      87
Derivative (exact category)      131
Derivative (poset)      47
Derivatively equivalent      134
Detect isomorphisms...      24
diamond      152
DIM      see "Dimension"
Dimension of a module      29
Dimension-function      34 63
Dimension-vector      7
Direct sum of categories      33
Direct sum of modules      24
Direct sum of posets      55
Directed quiver      102
Display-functor      74
Distributive spectroid      142
Dualizing (spectroid, aggregate)      94
Dumb-bell      151
Dynkin graph      57
Eigenline      124
Elementary (representation)      46
Elementary (transformation)      4
Epivalence of categories      18
Equivalence of categories      24
Equivalence of representations of posets      7
Exact category, structure      87
Extended Dynkin      57 120
Extension      24 89
Faithful (module)      44
Final subset of a poset      101
Finite corepresentation      85
Finite k-category      29
Finite presentation      22
Finitely (module)      34
Finitely (poset)      46
Finitely (ray-category)      146
Finitely free      21
Finitely generated      84
Finitely injective      111
Finitely presented      22
Finitely projective      22
Finitely represented (k-category)      142
Finitely spaced      34 35
Full subcategory      24
Full subposet      55
Fully faithful functor      24
Fundamental cone      66
Fundamental group      157
Galois covering      159
Generation indicator      84
gldim $\Box$      141
Grothendieck group      141
Head of an arrow      17
Hereditary      79 141
Ideal of a k-category      16
Idempotent      17
Identical path      17
Imaginary root      67
Immersion      21
ind $\Box$      101
Indecomposable      24
Indicator of relations      84
Induction      83
Inflation      87
Injective ($\mathscr{E}$-injective)      89
Injective envelope, envelopment      87
Injective-free      126
Interlaced      145
interval      31
Involutive representation      44
Isoclass      24
Isotropic generator      58
Isotropy group      65
k-category      16
k-category of paths      17
K-functor      16
Kernel of a k-functor      16
Linear matrix problem      8
Linearization (category)      16
Linearization (ray-category)      144
Local ring      32
Locally bounded      81
Locally finite quiver      81
Locular k-cateogry      25
Loop      17
Mapping cone      140
Matrix problem      8
Maximal dimension      34
Mesh - (sum, cateogry)      105
Minimal projective presentation      84
Minimal representation-infinite      149 155
mod $\Box$      22
Modular equivalence      23
Module (over a category)      18 19
Module of relations      84
Module represented by an object      19
Multilocular k-category      25
Multiplicative basis      43
Normal (monomorphism)      100
Null object      21
Omnipresent representation      55 63
Omnipresent root      58
One-sided matrix problem      8
Oriented tree      118
Origin of a path      17
Parallel paths      17
Path of length d      17
Pattern      107
pdim $\Box$      132
Penny-farthing      152
Piecewise hereditary      137
Pointwise finite      29
POSET      15
Positive form      56
Postprojective      104
Preinjective      104
Present (at a point)      39 46
Primitive idempotent      28
prin $\Box$      88
Prinjective module      88
pro $\Box$      22
Projection      21
Projection-functor      16
Projective ($\mathscr{E}-projective$)      90
Projective cover, covering      87
Projective dimension      101
Projective-free      126
Proper submodule      32
Pull-up, push-down      159
Quasi-inverse functor      24
Quasi-surjective functor      16
quiver      17
Quiver of a k-category      73 74
Radical      26
Ray, ray-category      143
Real root      60 66
Reflection      60
rep $\Box$      22
Repetition      81
Representation of a module      34
Representation of a poset      7
Representation of a quiver      20
Representation-quiver      101
Residue-category      16
Restriction of a unit form      56
Retraction      33
Root      52
S      130
S-category, S-functor, S-equivalence      141
S-sequence      140
Schurian      8
Section      33
Segment      8
Selfinjective      82
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