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Ternary commutator

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Bremner, Murray R.; Ortega, Juana Sánchez (25 October 2010), "The partially alternating ternary sum in an associative dialgebra",
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Devchand, Chandrashekar; Fairlie, David; Nuyts, Jean; Weingart, Gregor (6 November 2009), "Ternutator identities",
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Bremner, Murray R.; Peresi, Luiz A. (26 July 2012), "Higher identities for the ternary commutator",
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Bremner, Murray R.; Peresi, Luiz A. (1 April 2006), "Ternary analogues of Lie and Malcev algebras",
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Bremner, Murray R. (15 August 1998), "Identities for the Ternary Commutator",
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is equal to 0, is also 0. This statement makes 0 the
41: 366:Journal of Physics A: Mathematical and Theoretical 252:Journal of Physics A: Mathematical and Theoretical 141: 320:Journal of Physics A: Mathematical and General 171:= 3, whereas the 2-commutator is the ordinary 485: 8: 413:(1973), "Generalized Hamiltonian Dynamics", 142:{\displaystyle =abc-acb-bac+bca+cab-cba.\,} 492: 478: 377: 331: 309: 263: 241: 138: 40: 7: 446: 444: 298:Linear Algebra and Its Applications 14: 448: 396:10.1088/1751-8113/42/47/475209 350:10.1088/1751-8113/45/50/505201 282:10.1088/1751-8113/43/45/455215 160:, it is a special case of the 60: 42: 1: 464:. You can help Knowledge by 200:of the ternary commutator. 537: 443: 311:10.1016/j.laa.2005.09.004 435:10.1103/PhysRevD.7.2405 158:alternating ternary sum 521:Abstract algebra stubs 460:-related article is a 243:10.1006/jabr.1998.7433 203:The same happens when 143: 144: 184:When one or more of 39: 18:mathematical physics 427:1973PhRvD...7.2405N 388:2009JPhA...42U5209D 342:2012JPhA...45X5201B 274:2010JPhA...43S5215B 516:Ternary operations 230:Journal of Algebra 139: 22:ternary commutator 473: 472: 415:Physical Review D 198:absorbing element 26:ternary operation 24:is an additional 528: 494: 487: 480: 458:abstract algebra 452: 445: 437: 421:(8): 2405–2412, 406: 381: 360: 335: 314: 313: 292: 267: 246: 245: 152:Also called the 148: 146: 145: 140: 536: 535: 531: 530: 529: 527: 526: 525: 501: 500: 499: 498: 441: 411:Nambu, Yoichiro 409: 363: 317: 295: 249: 227: 224: 222:Further reading 181: 37: 36: 12: 11: 5: 534: 532: 524: 523: 518: 513: 503: 502: 497: 496: 489: 482: 474: 471: 470: 453: 439: 438: 407: 372:(47): 475209, 361: 326:(50): 505201, 315: 293: 258:(56): 455215, 247: 236:(2): 615–623, 223: 220: 219: 218: 217: 216: 180: 177: 150: 149: 137: 134: 131: 128: 125: 122: 119: 116: 113: 110: 107: 104: 101: 98: 95: 92: 89: 86: 83: 80: 77: 74: 71: 68: 65: 62: 59: 56: 53: 50: 47: 44: 13: 10: 9: 6: 4: 3: 2: 533: 522: 519: 517: 514: 512: 509: 508: 506: 495: 490: 488: 483: 481: 476: 475: 469: 467: 463: 459: 454: 451: 447: 442: 436: 432: 428: 424: 420: 416: 412: 408: 405: 401: 397: 393: 389: 385: 380: 375: 371: 367: 362: 359: 355: 351: 347: 343: 339: 334: 329: 325: 321: 316: 312: 307: 303: 299: 294: 291: 287: 283: 279: 275: 271: 266: 261: 257: 253: 248: 244: 239: 235: 231: 226: 225: 221: 214: 210: 206: 202: 201: 199: 195: 191: 187: 183: 182: 178: 176: 174: 170: 166: 164: 159: 155: 135: 132: 129: 126: 123: 120: 117: 114: 111: 108: 105: 102: 99: 96: 93: 90: 87: 84: 81: 78: 75: 72: 69: 66: 63: 57: 54: 51: 48: 45: 35: 34: 33: 31: 30:triple system 27: 23: 19: 466:expanding it 455: 440: 418: 414: 369: 365: 323: 319: 301: 297: 255: 251: 233: 229: 212: 208: 204: 193: 189: 185: 168: 162: 157: 153: 151: 21: 15: 304:(1): 1–18, 165:-commutator 32:defined by 505:Categories 179:Properties 173:commutator 154:ternutator 379:0908.1738 333:1207.6312 265:1008.2721 124:− 88:− 76:− 511:Algebras 404:17246666 358:17037773 423:Bibcode 384:Bibcode 338:Bibcode 290:6636902 270:Bibcode 402:  356:  288:  20:, the 456:This 400:S2CID 374:arXiv 354:S2CID 328:arXiv 286:S2CID 260:arXiv 28:on a 462:stub 167:for 431:doi 392:doi 346:doi 306:doi 302:414 278:doi 238:doi 234:206 156:or 16:In 507:: 429:, 417:, 398:, 390:, 382:, 370:42 368:, 352:, 344:, 336:, 324:45 322:, 300:, 284:, 276:, 268:, 256:43 254:, 232:, 211:= 207:= 192:, 188:, 175:. 493:e 486:t 479:v 468:. 433:: 425:: 419:7 394:: 386:: 376:: 348:: 340:: 330:: 308:: 280:: 272:: 262:: 240:: 215:. 213:c 209:b 205:a 194:c 190:b 186:a 169:n 163:n 136:. 133:a 130:b 127:c 121:b 118:a 115:c 112:+ 109:a 106:c 103:b 100:+ 97:c 94:a 91:b 85:b 82:c 79:a 73:c 70:b 67:a 64:= 61:] 58:c 55:, 52:b 49:, 46:a 43:[

Index

mathematical physics
ternary operation
triple system
n-commutator
commutator
absorbing element
doi
10.1006/jabr.1998.7433
arXiv
1008.2721
Bibcode
2010JPhA...43S5215B
doi
10.1088/1751-8113/43/45/455215
S2CID
6636902
doi
10.1016/j.laa.2005.09.004
arXiv
1207.6312
Bibcode
2012JPhA...45X5201B
doi
10.1088/1751-8113/45/50/505201
S2CID
17037773
arXiv
0908.1738
Bibcode
2009JPhA...42U5209D

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