| Title:
|
Lie commutators in a free diassociative algebra (English) |
| Author:
|
Dzhumadil'daev, A.S. |
| Author:
|
Ismailov, N.A. |
| Author:
|
Orazgaliyev, A.T. |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
28 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
155-160 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Diassociative algebars |
| Keyword:
|
Leibniz elements |
| Keyword:
|
Dynkin-Specht-Wever criterion |
| MSC:
|
17A30 |
| MSC:
|
17A50 |
| idZBL:
|
Zbl 07300187 |
| idMR:
|
MR4162927 |
| . |
| Date available:
|
2021-03-03T08:45:52Z |
| Last updated:
|
2021-03-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148700 |
| . |
| Reference:
|
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| Reference:
|
[2] Bremner, M.R., Dotsenko, V.: Bilinear operations in the diassociative operad.preprint. |
| Reference:
|
[3] Demir, I., Misra, K.C., Stitzinger, E.: On some structures of Leibniz algebras.Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics, Contemporary Mathematics, 623, 2014, 41-54, MR 3288621 |
| Reference:
|
[4] Jacobson, N.: Lie algebras.1962, Interscience Publishers, Wiley, New York, Zbl 0121.27504, MR 0143793 |
| Reference:
|
[5] Loday, J.-L.: Une version non commutative des algébres de Lie: Les algébres de Leibniz.L'Enseignement Mathématique, 39, 2, 1993, 269-293, MR 1252069 |
| Reference:
|
[6] Loday, J.-L.: Algébres ayant deux opérations associatives: les digébres.Comptes rendus de l'Académie des Sciences, 321, 1995, 141-146, MR 1345436 |
| Reference:
|
[7] Loday, J.-L., Pirashvili, T.: Universal enveloping algebras of Leibniz algebras and (co)-homology.Mathematische Annalen, 296, 1, 1993, 139-158, Springer-Verlag, MR 1213376, 10.1007/BF01445099 |
| Reference:
|
[8] Loday, J.-L.: Dialgebras.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. MR 1860994, 10.1007/b80864 |
| . |
