An identity in the free Lie algebra. (English) Zbl 0682.17007
The author derives a nice formula involving the diagonal map, the multiplication map and the map in the criterion due to Specht-Wever to simplify the proofs of Friedrichs and Specht-Wever criteria for Lie elements in the enveloping algebra of a free Lie algebra.
Reviewer: Yu.A.Bakhturin
MSC:
| 17B55 | Homological methods in Lie (super)algebras |
Keywords:
universal enveloping algebras; tensor algebras; diagonal map; multiplication map; free Lie algebraReferences:
| [1] | Группы и алгебры Ли., Издат. ”Мир”, Мосцощ, 1976 (Руссиан). Алгебры Ли, свободные алгебры Ли и группы Ли. [Лие алгебрас, фрее Лие алгебрас анд Лие гроупс]; Едитед бы А. А. Кириллов анд А. И. Кострикин; Транслатед фром тхе Френч бы Ју. А. Бахтурин анд Г. И. Ол\(^{\приме}\)šанский; Ѐлементы Математики. [Елеменц оф Матхематицс]. |
| [2] | Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. · Zbl 0121.27504 |
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