Truncated 16-cell honeycomb: Difference between revisions

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In [[mathematical physics]], the '''ternary commutator''' is an additional [[ternary operation]] on a [[triple system]] defined by
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:<math>[a,b,c] = abc-acb-bac+bca+cab-cba. \, </math>
Also called the '''ternutator''' or '''alternating ternary sum''', it is a special case of the [[n-commutator|''n''-commutator]] for ''n'' = 3, whereas the 2-commutator is the ordinary [[commutator]].
 
==Further reading==
*{{Citation |last=Bremner |first=Murray R. |date=15 August 1998 |title=Identities for the Ternary Commutator |journal=Journal of Algebra |volume=206 |issue=2 |pages=615–623 |doi=10.1006/jabr.1998.7433 |url=http://math.usask.ca/~bremner/research/publications/Bitc.pdf}}
*{{Citation |last=Bremner |first=Murray R. |last2=Ortega |first2=Juana Sánchez |date=25 October 2010 |title=The partially alternating ternary sum in an associative dialgebra |journal=Journal of Physics A: Mathematical and Theoretical |volume=43 |issue=56 |doi=10.1088/1751-8113/43/45/455215 |arxiv=1008.2721}}
*{{Citation |last=Bremner |first=Murray R. |last2=Peresi |first2=Luiz A. |date=1 April 2006 |title=Ternary analogues of Lie and Malcev algebras |journal=Linear Algebra and its Applications |volume=414 |issue=1 |pages=1–18 |doi=10.1016/j.laa.2005.09.004 |url=http://math.usask.ca/~bremner/research/publications/BPtalma.pdf}}
*{{Citation |last=Bremner |first=Murray R. |last2=Peresi |first2=Luiz A. |date=26 July 2012 |title=Higher identities for the ternary commutator |arxiv=1207.6312}}
*{{Citation |last=Devchand |first=Chandrashekar |last2=Fairlie |first2=David |last3=Nuyts |first3=Jean |last4=Weingart |first4=Gregor |date=6 November 2009 |title=Ternutator identities |journal=Journal of Physics A: Mathematical and Theoretical |volume=42 |issue=47 |doi=10.1088/1751-8113/42/47/475209 |arxiv=0908.1738}}
*{{Citation |last=Nambu |first=Yoichiro |authorlink=Yoichiro Nambu |year=1973 |title=Generalized Hamiltonian Dynamics |journal=Physical Review D |volume=7 |issue=8 |pages=2405–2412 |doi=10.1103/PhysRevD.7.2405}}
 
[[Category:Algebras]]
[[Category:Ternary operations]]
 
{{abstract-algebra-stub}}

Latest revision as of 02:04, 3 November 2014

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