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Additive K-theory

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469: 228: 413: 142: 300: 320: 259: 162: 100: 80: 510: 238: 173: 46:. It is not, therefore, one theory but a way of creating additive or infinitesimal analogues of multiplicative theories. 503: 343: 534: 109: 496: 165: 33: 103: 264: 59: 25: 529: 334: 480: 433: 305: 244: 147: 85: 65: 523: 29: 234: 55: 40: 17: 468: 476: 484: 346: 308: 267: 247: 176: 150: 112: 88: 68: 223:{\displaystyle H_{\cdot }({{\mathfrak {g}}l}(A),k)} 407: 314: 294: 253: 222: 164:with only finitely many nonzero entries. Then the 156: 136: 94: 74: 439:. Dept. of Mathematics, University of Chicago. 408:{\displaystyle HC_{i}(A)\cong K_{i+1}^{+}(A).} 504: 8: 434:"Algebraic Cycles and Additive Chow Groups" 511: 497: 387: 376: 354: 345: 307: 277: 272: 266: 246: 192: 191: 190: 181: 175: 149: 144:be the algebra of infinite matrices over 115: 114: 113: 111: 87: 67: 424: 333:The additive K-functors are related to 137:{\displaystyle {{\mathfrak {g}}l}(A)} 7: 465: 463: 39:has everywhere been replaced by its 193: 116: 14: 467: 399: 393: 366: 360: 289: 283: 217: 208: 202: 187: 131: 125: 1: 432:Bloch, Spencer (2006-07-23). 233:has a natural structure of a 483:. You can help Knowledge by 295:{\displaystyle K_{i}^{+}(A)} 82:be an algebra over a field 551: 462: 337:groups by the isomorphism 28:in which, according to 449:B. Feigin, B. Tsygan. 409: 316: 296: 255: 224: 158: 138: 96: 76: 24:means some version of 410: 317: 297: 256: 225: 159: 139: 97: 77: 453:, LNM 1289, Springer 344: 306: 265: 245: 174: 166:Lie algebra homology 148: 110: 86: 66: 34:general linear group 392: 282: 237:. The space of its 104:characteristic zero 405: 372: 324:additive K-functor 312: 292: 268: 251: 239:primitive elements 220: 154: 134: 92: 72: 26:algebraic K-theory 492: 491: 451:Additive K-theory 315:{\displaystyle i} 254:{\displaystyle i} 157:{\displaystyle A} 95:{\displaystyle k} 75:{\displaystyle A} 22:additive K-theory 542: 513: 506: 499: 477:topology-related 471: 464: 454: 447: 441: 440: 438: 429: 414: 412: 411: 406: 391: 386: 359: 358: 321: 319: 318: 313: 301: 299: 298: 293: 281: 276: 260: 258: 257: 252: 229: 227: 226: 221: 201: 197: 196: 186: 185: 163: 161: 160: 155: 143: 141: 140: 135: 124: 120: 119: 101: 99: 98: 93: 81: 79: 78: 73: 550: 549: 545: 544: 543: 541: 540: 539: 520: 519: 518: 517: 460: 458: 457: 448: 444: 436: 431: 430: 426: 421: 350: 342: 341: 335:cyclic homology 304: 303: 302:and called the 263: 262: 243: 242: 177: 172: 171: 146: 145: 108: 107: 84: 83: 64: 63: 52: 12: 11: 5: 548: 546: 538: 537: 535:Topology stubs 532: 522: 521: 516: 515: 508: 501: 493: 490: 489: 472: 456: 455: 442: 423: 422: 420: 417: 416: 415: 404: 401: 398: 395: 390: 385: 382: 379: 375: 371: 368: 365: 362: 357: 353: 349: 311: 291: 288: 285: 280: 275: 271: 261:is denoted by 250: 231: 230: 219: 216: 213: 210: 207: 204: 200: 195: 189: 184: 180: 153: 133: 130: 127: 123: 118: 91: 71: 51: 48: 13: 10: 9: 6: 4: 3: 2: 547: 536: 533: 531: 528: 527: 525: 514: 509: 507: 502: 500: 495: 494: 488: 486: 482: 479:article is a 478: 473: 470: 466: 461: 452: 446: 443: 435: 428: 425: 418: 402: 396: 388: 383: 380: 377: 373: 369: 363: 355: 351: 347: 340: 339: 338: 336: 331: 329: 325: 309: 286: 278: 273: 269: 248: 240: 236: 214: 211: 205: 198: 182: 178: 170: 169: 168: 167: 151: 128: 121: 105: 89: 69: 61: 57: 49: 47: 45: 42: 38: 35: 31: 30:Spencer Bloch 27: 23: 19: 485:expanding it 474: 459: 450: 445: 427: 332: 327: 323: 235:Hopf algebra 232: 60:Boris Tsygan 56:Boris Feigin 53: 43: 36: 21: 15: 50:Formulation 41:Lie algebra 18:mathematics 524:Categories 419:References 241:of degree 54:Following 370:≅ 183:⋅ 530:K-theory 326:of  106:and let 62:, let 32:, the 475:This 437:(PDF) 481:stub 322:-th 58:and 102:of 16:In 526:: 330:. 44:gl 37:GL 20:, 512:e 505:t 498:v 487:. 403:. 400:) 397:A 394:( 389:+ 384:1 381:+ 378:i 374:K 367:) 364:A 361:( 356:i 352:C 348:H 328:A 310:i 290:) 287:A 284:( 279:+ 274:i 270:K 249:i 218:) 215:k 212:, 209:) 206:A 203:( 199:l 194:g 188:( 179:H 152:A 132:) 129:A 126:( 122:l 117:g 90:k 70:A

Index

mathematics
algebraic K-theory
Spencer Bloch
general linear group
Lie algebra
Boris Feigin
Boris Tsygan
characteristic zero
Lie algebra homology
Hopf algebra
primitive elements
cyclic homology
"Algebraic Cycles and Additive Chow Groups"
Stub icon
topology-related
stub
expanding it
v
t
e
Categories
K-theory
Topology stubs

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