IA-automorphisms and Lie Algebras related to the McCool group

2019/01/07 by C. E. Kofinas, Kofinas, C. E., V. Metaftsis +3
Mathematics · #17B01 #20F05 #20F40 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1901.01737

openalex publication_date 2019/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present work we investigate a subgroup I_n of the McCool group M_n. We show that I_n has solvable conjugacy problem. Next, we investigate its Lie Algebra gr(I_n) and we find a presentation for it. Finally we show that gr(I_n) is naturally embedded into the Andreadakis-Johnson Lie Algebra of the IA automorphisms of the free group F_n.

Citations

• On Basis-Conjugating Automorphisms of Free Groups

Related

• On the Andreadakis equality for a subgroup of the McCool group
• Quotient groups of IA-automorphisms of a free group of rank 3
• Dense and empty BNSR-invariants of the McCool groups
• The Andreadakis Problem for the McCool groups
• The group of automorphisms of the Jacobian algebra \mA_n