The Lower Central Series of the Quotient of a Free Algebra

2015/03/04 by Lev Haldar Kendrick, Kendrick, Lev, Gus Lonergan +1
Mathematics · #13N05 #14A22 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1503.01447

openalex publication_date 2015/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L_i(R) denote the i^th term of the lower central series of an associative algebra R, and let B_i(R)=L_i(R)/L_i+1(R). We show that B₂(ℂ/ P)≅ Ω²((ℂ/ P)_ab), for all homogeneous or quasihomogeneous P with square-free abelianization. Our approach generalizes that of Balagovic and Balasubramanian in 2010, which in turn developed from that of Dobrovolska, Kim, and Ma in 2007. We also use ideas of Feign and Shoikhet in 2006, who initiated the study of the groups B_i(R).

Related

• On properties of the lower central series of associative algebras
• On the filtration of a free algebra by its associative lower central series
• An upper bound for the lower central series quotients of a free associative algebra
• Lower Central Series Ideal Quotients Over F_p and Z
• The lower p-central series of a free profinite group and the shuffle algebra