Details:
Title  Some remarks on the Akivis algebras and the preLie algebras.  Author(s)  Yuri A. Blinkov, YuFu Chen  Type  Article in Journal  Abstract  In this paper, by using the CompositionDiamond lemma for nonassociative algebras invented by A. I. Shirshov in 1962, we give GröbnerShirshov bases for free PreLie algebras and the universal enveloping nonassociative algebra of an Akivis algebra, respectively. As applications, we show I.P. Shestakov’s result that any Akivis algebra is linear and D. Segal’s result that the set of all good words in X** forms a linear basis of the free PreLie algebra PLie(X) generated by the set X. For completeness, we give the details of the proof of Shirshov’s CompositionDiamond lemma for nonassociative algebras.  Keywords  nonassociative algebra, Akivis algebra, universal enveloping algebra, PreLie algebra, GröbnerShirshov basis  ISSN  00114642; 15729141/e 
URL 
http://link.springer.com/article/10.1007%2Fs105870110041y 
Language  English  Journal  Czech. Math. J.  Volume  61  Number  3  Pages  707720  Publisher  Springer, Berlin/Heidelberg  Year  2011  Edition  0  Translation 
No  Refereed 
No 
