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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
283:(1949), "Faithful representations of Lie algebras", 47:Ado's theorem states that every finite-dimensional 260:(1948), "On the representation of Lie algebras", 392: 339:Proceedings of the American Mathematical Society 200:"The representation of Lie algebras by matrices" 35:is a theorem characterizing finite-dimensional 279: 166:always has a linear representation that is a 379:, comments and a proof of Ado's theorem in 328: 231:American Mathematical Society Translations 73:. More precisely, the theorem states that 351: 147:While for the Lie algebras associated to 256: 14: 393: 228: 197: 183: 24: 116:The theorem was proved in 1935 by 100:isomorphic to a subalgebra of the 65:can be viewed as a Lie algebra of 25: 417: 370: 353:10.1090/s0002-9939-1966-0194482-0 262:Japanese Journal of Mathematics 142: 87:finite-dimensional vector space 334:"An addition to Ado's theorem" 186:Izv. Fiz.-Mat. Obsch. (Kazan') 13: 1: 177: 42: 7: 10: 422: 111: 158:, it does not imply that 406:Theorems about algebras 94:faithful representation 122:Kazan State University 286:Annals of Mathematics 198:Ado, Igor D. (1947), 194:. (Russian language) 79:linear representation 139:paper for a proof). 135:(see also the below 118:Igor Dmitrievich Ado 330:Hochschild, Gerhard 126:Nikolai Chebotaryov 63:characteristic zero 366:, pp. 202–203 137:Gerhard Hochschild 71:commutator bracket 18:Ado's Theorem 289:, Second Series, 258:Iwasawa, Kenkichi 168:local isomorphism 16:(Redirected from 413: 356: 355: 325: 276: 253: 226: 193: 149:classical groups 133:Kenkichi Iwasawa 29:abstract algebra 21: 421: 420: 416: 415: 414: 412: 411: 410: 391: 390: 373: 360:Nathan Jacobson 299:10.2307/1969352 227:translation in 180: 145: 124:, a student of 114: 67:square matrices 45: 23: 22: 15: 12: 11: 5: 419: 409: 408: 403: 389: 388: 372: 371:External links 369: 368: 367: 357: 326: 281:Harish-Chandra 277: 254: 210:(6): 159–173, 206:(in Russian), 195: 179: 176: 144: 141: 113: 110: 44: 41: 9: 6: 4: 3: 2: 418: 407: 404: 402: 399: 398: 396: 386: 382: 378: 377:Ado’s theorem 375: 374: 365: 361: 358: 354: 349: 345: 341: 340: 335: 331: 327: 324: 320: 316: 312: 308: 304: 300: 296: 292: 288: 287: 282: 278: 275: 271: 267: 263: 259: 255: 252: 248: 244: 240: 236: 232: 225: 221: 217: 213: 209: 205: 201: 196: 191: 187: 182: 181: 175: 173: 169: 165: 161: 157: 154: 150: 140: 138: 134: 129: 127: 123: 119: 109: 107: 103: 102:endomorphisms 99: 95: 91: 88: 84: 80: 76: 72: 68: 64: 60: 57: 53: 50: 40: 38: 34: 33:Ado's theorem 30: 19: 401:Lie algebras 384: 364:Lie Algebras 363: 343: 337: 290: 284: 265: 261: 234: 230: 207: 203: 189: 185: 172:linear group 163: 159: 155: 146: 143:Implications 130: 115: 105: 97: 92:, that is a 89: 82: 74: 58: 51: 46: 37:Lie algebras 32: 26: 381:Terence Tao 346:: 531–533, 268:: 405–426, 49:Lie algebra 395:Categories 385:What's new 178:References 69:under the 307:0003-486X 293:: 68–76, 243:0065-9290 237:(2): 21, 216:0042-1316 153:Lie group 96:, making 43:Statement 383:'s blog 332:(1966), 323:0028829 315:1969352 274:0032613 251:0030946 224:0027753 170:with a 112:History 85:, on a 81:ρ over 54:over a 321:  313:  305:  272:  249:  241:  222:  214:  192:: 1–43 77:has a 311:JSTOR 56:field 303:ISSN 239:ISSN 235:1949 212:ISSN 348:doi 295:doi 120:of 104:of 61:of 27:In 397:: 362:, 344:17 342:, 336:, 319:MR 317:, 309:, 301:, 291:50 270:MR 266:19 264:, 247:MR 245:, 233:, 220:MR 218:, 202:, 188:, 174:. 128:. 108:. 39:. 31:, 387:. 350:: 297:: 208:2 190:7 164:G 160:G 156:G 106:V 98:L 90:V 83:K 75:L 59:K 52:L 20:)

Index

Ado's Theorem
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

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