Homotopies of crossed complex morphisms of associative R-algebras

Akça İ. İ., Avcıoğlu O.

GEORGIAN MATHEMATICAL JOURNAL, cilt.28, sa.2, ss.163-172, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 28 Sayı: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1515/gmj-2019-2065
  • Dergi Adı: GEORGIAN MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.163-172
  • Anahtar Kelimeler: Crossed complex, homotopy, associative algebra, groupoid, derivation
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

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 = (H-n) is a sequence of R-linear maps H-n : C-n -> 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 to D has a groupoid structure with crossed complex morphisms as objects and homotopies as morphisms.