An Introduction to Homological AlgebraCambridge University Press, 1994 - Broj stranica: 450 The landscape of homological algebra has evolved over the past half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras is also described. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. |
Sadržaj
II | 1 |
III | 5 |
IV | 10 |
V | 15 |
VI | 18 |
VII | 25 |
VIII | 30 |
IX | 33 |
XLIV | 198 |
XLV | 203 |
XLVI | 206 |
XLVII | 216 |
XLIX | 219 |
L | 223 |
LI | 238 |
LII | 242 |
X | 38 |
XI | 43 |
XII | 49 |
XIII | 51 |
XIV | 58 |
XV | 66 |
XVI | 68 |
XVII | 73 |
XVIII | 76 |
XIX | 80 |
XX | 87 |
XXI | 91 |
XXII | 95 |
XXIII | 99 |
XXIV | 104 |
XXV | 111 |
XXVI | 115 |
XXVII | 120 |
XXVIII | 122 |
XXIX | 127 |
XXX | 131 |
XXXI | 135 |
XXXII | 141 |
XXXIII | 145 |
XXXIV | 150 |
XXXV | 153 |
XXXVI | 160 |
XXXVII | 167 |
XXXVIII | 171 |
XXXIX | 174 |
XL | 177 |
XLI | 182 |
XLII | 189 |
XLIII | 195 |
LIII | 248 |
LIV | 254 |
LV | 259 |
LVI | 270 |
LVII | 275 |
LVIII | 286 |
LIX | 294 |
LX | 300 |
LXI | 311 |
LXII | 319 |
LXIII | 326 |
LXIV | 330 |
LXV | 338 |
LXVI | 344 |
LXVII | 354 |
LXVIII | 362 |
LXIX | 369 |
LXX | 373 |
LXXI | 379 |
LXXII | 385 |
LXXIII | 390 |
LXXIV | 394 |
LXXV | 398 |
LXXVI | 402 |
LXXVII | 407 |
LXXVIII | 417 |
LXXIX | 421 |
LXXX | 423 |
LXXXI | 424 |
LXXXII | 427 |
LXXXIII | 429 |
432 | |
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8-functor abelian category abelian group acyclic bimodule bounded called central extension Ch(A chain complex chain homotopy chain homotopy equivalence chain map cochain cohomology cokernel colimit composition construction converges Corollary cotriple cyclic define Definition denote derived functors diagram differential dim(R direct sum double complex element exact functor exact triangle Example Exercise filtration finite flat forgetful functor formula g-mod H¹(g Hence Hochschild homology homomorphism ideal induces injective k-algebra kernel left adjoint left exact left R-module Lemma Lie algebra long exact sequence map f mod-R module morphism natural isomorphism natural map noetherian plex profinite projective resolution Proof quadrant quasi-isomorphism quotient R-mod R-module resp right exact right R-module semisimple sheaf sheaves short exact sequence Show simplicial object simplicial set spectral sequence split exact subgroup Suppose surjection Theorem topological space trivial universal central extension yields zero