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Ado's theorem

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Ado, Igor D. (1935), "Note on the representation of finite continuous groups by means of linear substitutions",
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there is nothing new in this, the general case is a deeper result. Applied to the real Lie algebra of a
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Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk
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has a faithful linear representation (which is not true in general), but rather that
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Ado, Igor D. (1949), "The representation of Lie algebras by matrices",
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The restriction on the characteristic was later removed by
272:(1949), "Faithful representations of Lie algebras", 36:Ado's theorem states that every finite-dimensional 249:(1948), "On the representation of Lie algebras", 381: 328:Proceedings of the American Mathematical Society 189:"The representation of Lie algebras by matrices" 24:is a theorem characterizing finite-dimensional 268: 155:always has a linear representation that is a 368:, comments and a proof of Ado's theorem in 317: 220:American Mathematical Society Translations 62:. More precisely, the theorem states that 340: 136:While for the Lie algebras associated to 245: 382: 217: 186: 172: 13: 105:The theorem was proved in 1935 by 89:isomorphic to a subalgebra of the 54:can be viewed as a Lie algebra of 14: 406: 359: 342:10.1090/s0002-9939-1966-0194482-0 251:Japanese Journal of Mathematics 131: 76:finite-dimensional vector space 323:"An addition to Ado's theorem" 175:Izv. Fiz.-Mat. Obsch. (Kazan') 1: 166: 31: 7: 10: 411: 100: 147:, it does not imply that 395:Theorems about algebras 83:faithful representation 111:Kazan State University 275:Annals of Mathematics 187:Ado, Igor D. (1947), 183:. (Russian language) 68:linear representation 128:paper for a proof). 124:(see also the below 107:Igor Dmitrievich Ado 319:Hochschild, Gerhard 115:Nikolai Chebotaryov 52:characteristic zero 355:, pp. 202–203 126:Gerhard Hochschild 60:commutator bracket 278:, Second Series, 247:Iwasawa, Kenkichi 157:local isomorphism 402: 345: 344: 314: 265: 242: 215: 182: 138:classical groups 122:Kenkichi Iwasawa 18:abstract algebra 410: 409: 405: 404: 403: 401: 400: 399: 380: 379: 362: 349:Nathan Jacobson 288:10.2307/1969352 216:translation in 169: 134: 113:, a student of 103: 56:square matrices 34: 12: 11: 5: 408: 398: 397: 392: 378: 377: 361: 360:External links 358: 357: 356: 346: 315: 270:Harish-Chandra 266: 243: 199:(6): 159–173, 195:(in Russian), 184: 168: 165: 133: 130: 102: 99: 33: 30: 9: 6: 4: 3: 2: 407: 396: 393: 391: 388: 387: 385: 375: 371: 367: 366:Ado’s theorem 364: 363: 354: 350: 347: 343: 338: 334: 330: 329: 324: 320: 316: 313: 309: 305: 301: 297: 293: 289: 285: 281: 277: 276: 271: 267: 264: 260: 256: 252: 248: 244: 241: 237: 233: 229: 225: 221: 214: 210: 206: 202: 198: 194: 190: 185: 180: 176: 171: 170: 164: 162: 158: 154: 150: 146: 143: 139: 129: 127: 123: 118: 116: 112: 108: 98: 96: 92: 91:endomorphisms 88: 84: 80: 77: 73: 69: 65: 61: 57: 53: 49: 46: 42: 39: 29: 27: 23: 22:Ado's theorem 19: 390:Lie algebras 373: 353:Lie Algebras 352: 332: 326: 279: 273: 254: 250: 223: 219: 196: 192: 178: 174: 161:linear group 152: 148: 144: 135: 132:Implications 119: 104: 94: 86: 81:, that is a 78: 71: 63: 47: 40: 35: 26:Lie algebras 21: 15: 370:Terence Tao 335:: 531–533, 257:: 405–426, 38:Lie algebra 384:Categories 374:What's new 167:References 58:under the 296:0003-486X 282:: 68–76, 232:0065-9290 226:(2): 21, 205:0042-1316 142:Lie group 85:, making 32:Statement 372:'s blog 321:(1966), 312:0028829 304:1969352 263:0032613 240:0030946 213:0027753 159:with a 101:History 74:, on a 70:ρ over 43:over a 310:  302:  294:  261:  238:  230:  211:  203:  181:: 1–43 66:has a 300:JSTOR 45:field 292:ISSN 228:ISSN 224:1949 201:ISSN 337:doi 284:doi 109:of 93:of 50:of 16:In 386:: 351:, 333:17 331:, 325:, 308:MR 306:, 298:, 290:, 280:50 259:MR 255:19 253:, 236:MR 234:, 222:, 209:MR 207:, 191:, 177:, 163:. 117:. 97:. 28:. 20:, 376:. 339:: 286:: 197:2 179:7 153:G 149:G 145:G 95:V 87:L 79:V 72:K 64:L 48:K 41:L

Index

abstract algebra
Lie algebras
Lie algebra
field
characteristic zero
square matrices
commutator bracket
linear representation
finite-dimensional vector space
faithful representation
endomorphisms
Igor Dmitrievich Ado
Kazan State University
Nikolai Chebotaryov
Kenkichi Iwasawa
Gerhard Hochschild
classical groups
Lie group
local isomorphism
linear group
"The representation of Lie algebras by matrices"
ISSN
0042-1316
MR
0027753
ISSN
0065-9290
MR
0030946
Iwasawa, Kenkichi

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