On lower central series quotients of finitely generated algebras over \(\mathbb Z\).

DOI10.1016/j.jalgebra.2014.10.018zbMath1327.16029arXiv1309.1237OpenAlexW2021191228MaRDI QIDQ479768

Kathleen Zhou, Katherine Cordwell, Teng Fei

Publication date: 5 December 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.1237

zbMATH Keywords

representationstorsion subgroupnon-commutative algebrasJordan-Hölder serieslower central seriestorsion elements

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Homological dimension (category-theoretic aspects) (18G20) Solvable, nilpotent (super)algebras (17B30) Graded rings and modules (associative rings and algebras) (16W50) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60) Identities other than those of matrices over commutative rings (16R40)

Related Items

The torsion subgroup of the additive group of a Lie nilpotent associative ring of class 3., Some products of commutators in an associative ring, Relations in universal Lie nilpotent associative algebras of class 4

Uses Software

• Magma

Cites Work

• On the filtration of a free algebra by its associative lower central series.
• On the lower central series quotients of a graded associative algebra.
• On the lower central series of an associative algebra (with an appendix by Pavel Etingof).
• New results on the lower central series quotients of a free associative algebra.
• On universal Lie nilpotent associative algebras.
• The Magma algebra system. I: The user language
• The torsion subgroup of the additive group of a Lie nilpotent associative ring of class 3.
• Lower central series of a free associative algebra over the integers and finite fields.
• Lower central series of free algebras in symmetric tensor categories.
• The additive group of a Lie nilpotent associative ring.
• On \([A,A/[A[A,A]]\) and on a \(W_n\)-action on the consecutive commutators of free associative algebras.]
• An Algebro-geometric Construction of Lower Central Series of Associative Algebras
• An Upper Bound for the Lower Central Series Quotients of a Free Associative Algebra
• IRREDUCIBLE REPRESENTATIONS OF INFINITE-DIMENSIONAL LIE ALGEBRAS OF CARTAN TYPE
• Relations in universal Lie nilpotent associative algebras of class 4
• On rings whose associated Lie rings are nilpotent