Homotopies of crossed complex morphisms of associative R-algebras

AKÇA İ. İ., Avcloǧlu O.

Georgian Mathematical Journal, vol.28, no.2, pp.163-172, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.1515/gmj-2019-2065
  • Journal Name: Georgian Mathematical Journal
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.163-172
  • Keywords: associative algebra, Crossed complex, derivation, groupoid, homotopy
  • Uşak University Affiliated: Yes

Abstract

In this study, given two crossed complexes C and D of associative R-algebras and a crossed complex morphism f:C→D, we construct a homotopy as a pair (H,f), where H=(Hn) is a sequence of R-linear maps Hn:Cn→Dn+1. Then we show that for a fixed pair C and D of crossed complexes of associative R-algebras, the family of all homotopies between crossed complex morphisms from C C to D has a groupoid structure with crossed complex morphisms as objects and homotopies as morphisms.