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Affine representation

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320: 22: 385: 390: 32: 361: 90: 62: 69: 47: 380: 76: 354: 262: 58: 267: 230: 180: 395: 347: 226: 137: 83: 289: 153: 145: 120: 299: 250: 211: 203: 141: 331: 303: 374: 225: + 1, an affine representation may be thought of as a particular kind of 39: 242: 161: 130: 280:
Remm, Elisabeth; Goze, Michel (2003), "Affine Structures on abelian Lie Groups",
319: 169: 112: 21: 123: 327: 245:; in that case, we actually have a linear representation in dimension 294: 15: 229:. We may ask whether a given affine representation has a 335: 43: 237:. If it does, we may take that as origin and regard 355: 8: 168:). Similarly, an affine representation of a 48:introducing citations to additional sources 362: 348: 293: 38:Relevant discussion may be found on the 386:Representation theory of Lie algebras 7: 316: 314: 217:Since the affine group in dimension 391:Representation theory of Lie groups 282:Linear Algebra and its Applications 14: 318: 202:An example is the action of the 31:relies largely or entirely on a 20: 221:is a matrix group in dimension 249:. This reduction depends on a 1: 304:10.1016/S0024-3795(02)00452-4 334:. You can help Knowledge by 412: 313: 233:in the given affine space 268:Projective representation 195:) of the affine group of 181:Lie algebra homomorphism 59:"Affine representation" 330:-related article is a 253:question, in general. 227:linear representation 117:affine representation 44:improve this article 381:Homological algebra 187:to the Lie algebra 154:automorphism group 146:group homomorphism 343: 342: 109: 108: 94: 403: 364: 357: 350: 322: 315: 306: 297: 251:group cohomology 104: 101: 95: 93: 52: 24: 16: 411: 410: 406: 405: 404: 402: 401: 400: 371: 370: 369: 368: 311: 279: 276: 259: 212:Euclidean space 204:Euclidean group 105: 99: 96: 53: 51: 37: 25: 12: 11: 5: 409: 407: 399: 398: 393: 388: 383: 373: 372: 367: 366: 359: 352: 344: 341: 340: 323: 309: 308: 275: 272: 271: 270: 265: 258: 255: 107: 106: 42:. Please help 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 408: 397: 396:Algebra stubs 394: 392: 389: 387: 384: 382: 379: 378: 376: 365: 360: 358: 353: 351: 346: 345: 339: 337: 333: 329: 324: 321: 317: 312: 305: 301: 296: 291: 287: 283: 278: 277: 273: 269: 266: 264: 261: 260: 256: 254: 252: 248: 244: 240: 236: 232: 228: 224: 220: 215: 213: 209: 205: 200: 198: 194: 190: 186: 182: 178: 174: 171: 167: 163: 159: 155: 151: 147: 143: 139: 135: 132: 128: 125: 122: 118: 114: 103: 92: 89: 85: 82: 78: 75: 71: 68: 64: 61: –  60: 56: 55:Find sources: 49: 45: 41: 35: 34: 33:single source 29:This article 27: 23: 18: 17: 336:expanding it 325: 310: 295:math/0105023 285: 281: 263:Group action 246: 243:vector space 238: 234: 222: 218: 216: 207: 201: 196: 192: 188: 184: 176: 172: 165: 162:affine group 157: 149: 133: 131:affine space 126: 116: 110: 97: 87: 80: 73: 66: 54: 30: 288:: 215–230, 231:fixed point 170:Lie algebra 121:topological 113:mathematics 375:Categories 274:References 138:continuous 70:newspapers 210:) on the 124:Lie group 40:talk page 257:See also 100:May 2024 328:algebra 152:to the 84:scholar 160:, the 142:smooth 129:on an 86:  79:  72:  65:  57:  326:This 290:arXiv 241:as a 183:from 179:is a 148:from 136:is a 119:of a 115:, an 91:JSTOR 77:books 332:stub 164:Aff( 63:news 300:doi 286:360 214:E. 189:aff 175:on 156:of 111:In 46:by 377:: 298:, 284:, 206:E( 199:. 144:) 363:e 356:t 349:v 338:. 307:. 302:: 292:: 247:n 239:A 235:A 223:n 219:n 208:n 197:A 193:A 191:( 185:g 177:A 173:g 166:A 158:A 150:G 140:( 134:A 127:G 102:) 98:( 88:· 81:· 74:· 67:· 50:. 36:.

Index


single source
talk page
improve this article
introducing citations to additional sources
"Affine representation"
news
newspapers
books
scholar
JSTOR
mathematics
topological
Lie group
affine space
continuous
smooth
group homomorphism
automorphism group
affine group
Lie algebra
Lie algebra homomorphism
Euclidean group
Euclidean space
linear representation
fixed point
vector space
group cohomology
Group action
Projective representation

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