Representability of actions in the category of (Pre)crossed modules in Leibniz algebras

Atik M., Aytekin A., Uslu E. O.

COMMUNICATIONS IN ALGEBRA, vol.45, no.5, pp.1825-1841, 2017 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 45 Issue: 5
  • Publication Date: 2017
  • Doi Number: 10.1080/00927872.2016.1226853
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1825-1841
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

We investigate the representability of actions in the category of (pre)crossed modules in Leibniz algebras. For this, we construct an actor of a (pre)cat(1)-Leibniz algebra and then by using the natural equivalence of the categories of (pre)cat(1)-Leibniz algebras and that of (pre)crossed modules, we construct the split extension classifier of the corresponding (pre)crossed module.