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The loop of formal power series with noncommutative coefficients under substitution

Authors
  • Pérez-Izquierdo, J. M.
Type
Published Article
Journal
São Paulo Journal of Mathematical Sciences
Publisher
Springer International Publishing
Publication Date
Apr 22, 2019
Volume
13
Issue
1
Pages
133–157
Identifiers
DOI: 10.1007/s40863-019-00131-w
Source
Springer Nature
Keywords
License
Yellow

Abstract

The set of formal power series with coefficients in an associative but noncommutative algebra becomes a loop with the substitution product. We study this loop by describing certain Lie and Sabinin algebras related to it. Some examples of Lie algebras satisfying the standard identities of degrees 5 and 6 appear naturally.

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