Taylor expansions of groups and filteredformality
Abstract
Let $G$ be a finitely generated group, and let $\Bbbk{G}$ be its group algebra over a field of characteristic $0$. A Taylor expansion is a certain type of map from $G$ to the degree completion of the associated graded algebra of $\Bbbk{G}$ which generalizes the Magnus expansion of a free group. The group $G$ is said to be filteredformal if its Malcev Lie algebra is isomorphic to the degree completion of its associated graded Lie algebra. We show that $G$ is filteredformal if and only if it admits a Taylor expansion, and derive some consequences.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 DOI:
 10.48550/arXiv.1905.10355
 arXiv:
 arXiv:1905.10355
 Bibcode:
 2019arXiv190510355S
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Rings and Algebras
 EPrint:
 19 pages