Knowledge

Quadratic algebra

Source 📝

371: 135: 412: 296: 288: 234: 405: 329: 91: 260: 436: 398: 154:
If the subspace of relations is instead allowed to also contain inhomogeneous degree 2 elements, i.e.
341: 325: 431: 292: 219: 31:
generated by degree one elements, with defining relations of degree 2. It was pointed out by
351: 282: 245: 223: 28: 306: 302: 382: 249: 215: 141: 40: 425: 36: 256: 227: 59: 355: 370: 238: 20: 32: 346: 378: 193:
and with quadratic relations forming the orthogonal complement of
287:. University Lecture Series. Vol. 37. Providence, R.I.: 39:. The most important class of graded quadratic algebras is 35:
that such algebras play an important role in the theory of
330:"Quadratic duals, Koszul dual functors, and applications" 386: 248:
of a finite-dimensional vector space equipped with a
94: 281:Polishchuk, Alexander; Positselski, Leonid (2005). 129: 73:and a subspace of homogeneous quadratic relations 230:are graded quadratic (in fact, Koszul) algebras. 406: 8: 124: 118: 413: 399: 345: 113: 93: 130:{\displaystyle A=T(V)/\langle S\rangle } 324:Mazorchuk, Volodymyr; Ovsienko, Serge; 273: 189:: the quadratic algebra generated by 7: 367: 365: 174:), this construction results in a 140:and inherits its grading from the 14: 369: 263:is a filtered quadratic algebra. 252:is a filtered quadratic algebra. 241:is a filtered quadratic algebra. 110: 104: 1: 356:10.1090/S0002-9947-08-04539-X 289:American Mathematical Society 385:. You can help Knowledge by 235:universal enveloping algebra 181:A graded quadratic algebra 453: 364: 176:filtered quadratic algebra 259:of a finite-dimensional 237:of a finite-dimensional 226:of a finite-dimensional 53:graded quadratic algebra 334:Trans. Amer. Math. Soc. 261:symplectic vector space 381:-related article is a 131: 16:Process in mathematics 132: 92: 326:Stroppel, Catharina 58:is determined by a 284:Quadratic algebras 185:as above admits a 127: 394: 393: 298:978-0-8218-3834-1 220:symmetric algebra 25:quadratic algebra 444: 415: 408: 401: 373: 366: 358: 349: 340:(3): 1129–1172, 311: 310: 278: 246:Clifford algebra 224:exterior algebra 136: 134: 133: 128: 117: 29:filtered algebra 452: 451: 447: 446: 445: 443: 442: 441: 422: 421: 420: 419: 362: 347:math.RT/0603475 323: 320: 318:Further reading 315: 314: 299: 280: 279: 275: 270: 211: 90: 89: 72: 49: 41:Koszul algebras 17: 12: 11: 5: 450: 448: 440: 439: 434: 424: 423: 418: 417: 410: 403: 395: 392: 391: 374: 360: 359: 319: 316: 313: 312: 297: 272: 271: 269: 266: 265: 264: 253: 250:quadratic form 242: 231: 216:tensor algebra 210: 207: 187:quadratic dual 142:tensor algebra 138: 137: 126: 123: 120: 116: 112: 109: 106: 103: 100: 97: 70: 62:of generators 48: 45: 37:quantum groups 15: 13: 10: 9: 6: 4: 3: 2: 449: 438: 437:Algebra stubs 435: 433: 430: 429: 427: 416: 411: 409: 404: 402: 397: 396: 390: 388: 384: 380: 375: 372: 368: 363: 357: 353: 348: 343: 339: 335: 331: 327: 322: 321: 317: 308: 304: 300: 294: 291:. p. 6. 290: 286: 285: 277: 274: 267: 262: 258: 254: 251: 247: 243: 240: 236: 232: 229: 225: 221: 217: 213: 212: 208: 206: 204: 200: 196: 192: 188: 184: 179: 177: 173: 169: 165: 161: 157: 152: 150: 146: 143: 121: 114: 107: 101: 98: 95: 88: 87: 86: 84: 80: 76: 69: 65: 61: 57: 54: 46: 44: 42: 38: 34: 30: 26: 22: 387:expanding it 376: 361: 337: 333: 283: 276: 257:Weyl algebra 228:vector space 202: 198: 194: 190: 186: 182: 180: 175: 171: 167: 163: 159: 155: 153: 148: 144: 139: 82: 78: 74: 67: 63: 60:vector space 55: 52: 50: 24: 18: 239:Lie algebra 21:mathematics 426:Categories 268:References 47:Definition 33:Yuri Manin 125:⟩ 119:⟨ 432:Algebras 328:(2009), 209:Examples 379:algebra 307:2177131 85:. Thus 305:  295:  377:This 342:arXiv 27:is a 383:stub 293:ISBN 255:The 244:The 233:The 222:and 214:The 151:). 23:, a 352:doi 338:361 197:in 166:⊕ ( 19:In 428:: 350:, 336:, 332:, 303:MR 301:. 218:, 205:. 201:⊗ 178:. 170:⊗ 162:⊕ 158:⊂ 81:⊗ 77:⊂ 66:= 51:A 43:. 414:e 407:t 400:v 389:. 354:: 344:: 309:. 203:V 199:V 195:S 191:V 183:A 172:V 168:V 164:V 160:k 156:S 149:V 147:( 145:T 122:S 115:/ 111:) 108:V 105:( 102:T 99:= 96:A 83:V 79:V 75:S 71:1 68:A 64:V 56:A

Index

mathematics
filtered algebra
Yuri Manin
quantum groups
Koszul algebras
vector space
tensor algebra
tensor algebra
symmetric algebra
exterior algebra
vector space
universal enveloping algebra
Lie algebra
Clifford algebra
quadratic form
Weyl algebra
symplectic vector space
Quadratic algebras
American Mathematical Society
ISBN
978-0-8218-3834-1
MR
2177131
Stroppel, Catharina
"Quadratic duals, Koszul dual functors, and applications"
arXiv
math.RT/0603475
doi
10.1090/S0002-9947-08-04539-X
Stub icon

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.