SavedAdd your journal

Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2026 / Cilt: 9 Sayı: 1

Homotopy of Lie-Rinehart Crossed Module Morphisms

Lie-Rinehart Çapraz Modül Morfizimlerinin Homotopisi

Ayşe Çobankaya(çukurova üniversitesi fen edebiyat fakültesi matematik bölümü)
Selim Çetin(MEHMET AKİF ERSOY ÜNİVERSİTESİ)
Pages
202–212
Publication Date
2019-06-28
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Additionally a groupoid structure of Lie- Rinehart crossed module morphisms and their homotopies.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper our aim is to give the concept homotopy of morphisms of Lie-Rinehart crossed modules.
📊
Key Findings & Data:We show that the homotopy relation gives rise to an equivalence relation.
💡
Conclusion & Impact:Additionally a groupoid structure of Lie- Rinehart crossed module morphisms and their homotopies.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Lie-Rinehart Cebir · Çapraz Modüller · Türevler

Abstract

In this paper our aim is to give the concept homotopy of morphisms of Lie-Rinehart crossed modules. We show that the homotopy relation gives rise to an equivalence relation. Additionally a groupoid structure of Lie- Rinehart crossed module morphisms and their homotopies.

Özet

Bu makalede amacımız Lie-Rinehart çapraz modüllerin morfizmlerinin homotopi kavramını vermektir. Homotopi bağıntısı bir denklik bağıntısı oluşturduğunu, buna ek olarak Lie- Rinehart çapraz modül morfizmleri ve homotopileri bir groupoid yapısı olduğunu gösterdik.

🔖

Cite This Article

Çobankaya, A., Çetin, S. (2019). Homotopy of Lie-Rinehart Crossed Module Morphisms. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 9 Sayı: 1, 202–212. https://ajindex.com/articles/1352312

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (2)

  1. Akça, İ.İ., Sidal, Y., Homotopies of Lie crossed module morphisms, arXiv: 1609.09297v1[math.CT], 2016.[2] Brown, R., and Higgings, P. J., Tensor Products and Homotopies for w− groupoids andcrossed complexes, Journal of Pure and Applied Algebra 47, 1-33, 1987.[3] Cabello, J.G. and Garzon, A.R., Closed model structures foralgebraic models for n−types, Journal of Pure and Applied Algebra 103 (3), 287-302, 1995.[4] Casas, J.M., Ladra, M., Pirashvili, T., Crossed modules for Lie-Rinehart algebras,Journal of Algebra, 274, 192-201, 2004.[5] Casas, J.M., Ladra, M., Pirashvili, T., Triple cohomology of Lie-Rinehart algebras andthe canonical class of associative algebras, Journal of Algebra, 291, 144-163, 2005.[6] Herz, J., Pseudo-algbres de Lie, C. R. Acad. Sci. Paris, 236, 1935-1937, 1953.[7] Huebschmann, J., Poisson cohomology and quantization, J. Reine Angew Math.408,57-113, 1990.[8] Mackenzie, K., Lie Groupoids and Lie algebroids in differential geometry, London math.soc. lecture note ser., vol. 124, Cambridge Univ. Press, 1987.[9] Whitehead, J.H.C., Note on a previous paper entitled On adding relations to homotopygroups, Ann. of Math. (2), 47, 806-810, 1946.[10] Whitehead, J.H.C., Combinatorial Homotopy I and II, Bull. Amer. Math. Soc., 55,231-245 and 453-456, 1949.[11] Whitehead, J.H.C., On adding relations to homotopy groups, Ann. of Math. (2), 42, 409-428, 1941.
  2. Akça, İ.İ., Sidal, Y., Homotopies of Lie crossed module morphisms, arXiv: 1609.09297v1[math.CT], 2016.[2] Brown, R., and Higgings, P. J., Tensor Products and Homotopies for w− groupoids andcrossed complexes, Journal of Pure and Applied Algebra 47, 1-33, 1987.[3] Cabello, J.G. and Garzon, A.R., Closed model structures foralgebraic models for n−types, Journal of Pure and Applied Algebra 103 (3), 287-302, 1995.[4] Casas, J.M., Ladra, M., Pirashvili, T., Crossed modules for Lie-Rinehart algebras,Journal of Algebra, 274, 192-201, 2004.[5] Casas, J.M., Ladra, M., Pirashvili, T., Triple cohomology of Lie-Rinehart algebras andthe canonical class of associative algebras, Journal of Algebra, 291, 144-163, 2005.[6] Herz, J., Pseudo-algbres de Lie, C. R. Acad. Sci. Paris, 236, 1935-1937, 1953.[7] Huebschmann, J., Poisson cohomology and quantization, J. Reine Angew Math.408,57-113, 1990.[8] Mackenzie, K., Lie Groupoids and Lie algebroids in differential geometry, London math.soc. lecture note ser., vol. 124, Cambridge Univ. Press, 1987.[9] Whitehead, J.H.C., Note on a previous paper entitled On adding relations to homotopygroups, Ann. of Math. (2), 47, 806-810, 1946.[10] Whitehead, J.H.C., Combinatorial Homotopy I and II, Bull. Amer. Math. Soc., 55,231-245 and 453-456, 1949.[11] Whitehead, J.H.C., On adding relations to homotopy groups, Ann. of Math. (2), 42, 409-428, 1941.