The theorems on freedom for relatively free Lie algebras and groups with a single relation

2021/01/14 by Alexander Krasnikov, Krasnikov, Alexander
Mathematics · #17B01 #20F19 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:17B01 #msc:20F19

paper · pdf · doi:10.48550/arxiv.2101.05648

26 pages, in Russian

openalex publication_date 2021/01/14 · arxiv created 2021/07/26 · arxiv updated 2021/07/27 · openalex created_date 2021/08/02 · openalex updated_date 2026/07/28

Abstract

In this paper we prove the theorem on freedom for relatively free groups with a single relation (analogous with the well-known result of Magnus) and the theorem on freedom for relatively free Lie algebras with a single relation (analogous with the well-known result of Shirshov).

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