Lie commutators in a free diassociative algebra
A.S. Dzhumadil'daev; N.A. Ismailov; A.T. Orazgaliyev
Communications in Mathematics (2020)
- Volume: 28, Issue: 2, page 155-160
- ISSN: 1804-1388
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topDzhumadil'daev, A.S., Ismailov, N.A., and Orazgaliyev, A.T.. "Lie commutators in a free diassociative algebra." Communications in Mathematics 28.2 (2020): 155-160. <http://eudml.org/doc/297376>.
@article{Dzhumadildaev2020,
abstract = {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.},
author = {Dzhumadil'daev, A.S., Ismailov, N.A., Orazgaliyev, A.T.},
journal = {Communications in Mathematics},
keywords = {Diassociative algebars; Leibniz elements; Dynkin-Specht-Wever criterion},
language = {eng},
number = {2},
pages = {155-160},
publisher = {University of Ostrava},
title = {Lie commutators in a free diassociative algebra},
url = {http://eudml.org/doc/297376},
volume = {28},
year = {2020},
}
TY - JOUR
AU - Dzhumadil'daev, A.S.
AU - Ismailov, N.A.
AU - Orazgaliyev, A.T.
TI - Lie commutators in a free diassociative algebra
JO - Communications in Mathematics
PY - 2020
PB - University of Ostrava
VL - 28
IS - 2
SP - 155
EP - 160
AB - 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.
LA - eng
KW - Diassociative algebars; Leibniz elements; Dynkin-Specht-Wever criterion
UR - http://eudml.org/doc/297376
ER -
References
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- Loday, J.-L., 10.1007/b80864, 2001, 7-66, Springer-Verlag, Berlin, Chapter in: Dialgebras and related operads, Lecture Notes in Mathematics, Vol. 1763, J.-L. Loday, F. Chapoton, F. Goichot, and A. Frabetti. (2001) MR1860994DOI10.1007/b80864
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