New results on the lower central series quotients of a free associative algebra.

DOI10.1016/j.jalgebra.2009.12.024zbMath1200.16031arXiv0902.4899OpenAlexW2033567572MaRDI QIDQ961034

Noah Arbesfeld, David Jordan

Publication date: 29 March 2010

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

Full work available at URL: https://arxiv.org/abs/0902.4899

zbMATH Keywords

non-commutative algebrasfree algebraslower central seriesassociated graded Lie algebrasLie algebras of polynomial vector fieldstensor field modules

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Growth rate, Gelfand-Kirillov dimension (16P90) Lie algebras of vector fields and related (super) algebras (17B66) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Graded rings and modules (associative rings and algebras) (16W50) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60)

Related Items

The lower central series of the symplectic quotient of a free associative algebra., Lower central series of a free associative algebra over the integers and finite fields., Lower central series of free algebras in symmetric tensor categories., On lower central series quotients of finitely generated algebras over \(\mathbb Z\)., The torsion subgroup of the additive group of a Lie nilpotent associative ring of class 3., Relations in universal Lie nilpotent associative algebras of class 4

Uses Software

• Magma

Cites Work

• On the lower central series of an associative algebra (with an appendix by Pavel Etingof).
• The Magma algebra system. I: The user language
• On \([A,A/[A[A,A]]\) and on a \(W_n\)-action on the consecutive commutators of free 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
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