Finely homogeneous computations in free Lie algebras.

Andary, Philippe

Displaying similar documents to “Finely homogeneous computations in free Lie algebras.”

An algorithm for analysis of the structure of finitely presented Lie algebras.

Gerdt, Vladimir P., Kornyak, Vladimir V. (1997)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

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Some remarks on the Akivis algebras and the Pre-Lie algebras

Yuqun Chen, Yu Li (2011)

Czechoslovak Mathematical Journal

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In this paper, by using the Composition-Diamond lemma for non-associative algebras invented by A. I. Shirshov in 1962, we give Gröbner-Shirshov bases for free Pre-Lie algebras and the universal enveloping non-associative 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 Pre-Lie algebra $PLie (X)$ generated by the set $X$ . For completeness,...

Lie commutators in a free diassociative algebra

A.S. Dzhumadil&amp;#039;daev, N.A. Ismailov, A.T. Orazgaliyev (2020)

Communications in Mathematics

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We give a criterion for Leibniz elements in a free diassociative algebra. In the diassociative case one can consider two versions of Lie commutators. We give criterions for elements of diassociative algebras to be Lie under these commutators. One of them corresponds to Leibniz elements. It generalizes the Dynkin-Specht-Wever criterion for Lie elements in a free associative algebra.

On maximal subalgebras of central simple Malcev algebras.

Alberto C. Elduque Palomo (1986)

Extracta Mathematicae

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In this paper the structure of the maximal elements of the lattice of subalgebras of central simple non-Lie Malcev algebras is considered. Such maximal subalgebras are studied in two ways: first by using theoretical results concerning Malcev algebras, and second by using the close connection between these simple non-Lie Malcev algebras and the Cayley-Dickson algebras, which have been extensively studied (see [4]).