×
Drensky, Vesselin; Piacentini Cattaneo, Giulia Maria

Varieties of metabelian Leibniz algebras. (English) Zbl 1025.17001

J. Algebra Appl. 1, No. 1, 31-50 (2002).
The authors commence the systematic study of Leibniz algebras from the point of view of the combinatorial theory of algebras with polynomial identities. Then, the language of \(T\)-ideals (or equivalently, varieties of algebras) is used to describe the free metabelian Leibniz algebras, the complete list of all left-nilpotent of class \(2\) varieties of Leibniz algebras is presented and the asymptotic behavior of all metabelian varieties is determined.
Reviewer: Marek Golasiński (Toruń)

Cited in 1 Review
Cited in 13 Documents

MSC:

17A32 Leibniz algebras
17B01 Identities, free Lie (super)algebras
17A50 Free nonassociative algebras
17B30 Solvable, nilpotent (super)algebras

Keywords:

Leibniz algebra; polynomial identities; relatively free algebra; metabelian identity; Hilbert series
Cite Review PDF
Full Text: DOI

References:

[1] Bahturin Yu. A., Trudy Sem. Petrovsk. 1 pp 45– (1975)
[2] Drensky V., Mat. Sb. 115 pp 98– (1981)
[3] Drensky V., Serdica 8 pp 20– (1982)
[4] Drensky V., Pliska, Studia Math. Bulg. 8 pp 94– (1986)
[5] Drensky V., Serdica 15 pp 293– (1989)
[6] Kemer A. R., Izv. Vyssh. Uchebn. Zaved. 6 pp 71– (1989)
[7] Loday J.-L., Enseign. Math. 39 pp 269– (1993)
[8] DOI: 10.1007/BF01445099 · Zbl 0821.17022 · doi:10.1007/BF01445099
[9] DOI: 10.1080/00927879808826139 · Zbl 0892.17002 · doi:10.1080/00927879808826139
[10] Pchelintsev S. V., Mat. Sb. 115 pp 179– (1981)
[11] DOI: 10.1016/0022-4049(92)90083-R · Zbl 0746.16016 · doi:10.1016/0022-4049(92)90083-R
[12] Umirbaev U. U., Sibirsk. Mat. Zh. 34 (6) pp 179– (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.