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Crossed Corner of Lie Algebras

Yıl 2025, Cilt: 14 Sayı: 2, 877 - 886, 30.06.2025

Işıl Zekiye Kurtuluş Özgün Gürmen Alansal

https://doi.org/10.17798/bitlisfen.1606755

Öz

In this work, we explore the concept of crossed corners in lie algebras and establish a connection between the category of crossed corners of lie algebras and the category of reduced simplicial lie algebras with Moore complex has length 2.

Anahtar Kelimeler

lie algebra crossed module crossed corner

Etik Beyan

The study is complied with research and publication ethics.

Teşekkür

This study was developed from Işıl Zekiye Kurtuluş’s master's thesis.

Kaynakça

  • J. H. C. Whitehead, “Combinatorial Homotopy II”, Bulletin of the American Mathematical Society, 55, 1949, pp. 453-496.
  • C. Kassel, and J. L. Loday, “Extensions Centrales D’algébres de Lie”, Annales de l’institut Fourier, 33,1982, pp.119-142.
  • G. J. Ellis, “Higher Dimensional Crossed Modules of Algebras”, Journal of Pure and Applied Algebra, 52, 1988, pp. 277-282.
  • I. I. Akça, and Z. Arvasi, “Simplicial and Crossed Lie Algebras, Homology”, Homotopy and Applications, 4 (1), 2002, pp. 43-57.
  • E. Ulualan, and E. Uslu, “Quadratic Modules for Lie Algebras”, Hacettepe Journal of Mathematics and Statistics, 40 (3), 2011, pp. 409-419.
  • E. Özel, and U. E. Arslan, “On Quasi Quadratic Modules of Lie Algebras”, Journal of New Theory, (41), 2022, pp. 62-69.
  • E. Ulualan, “Braiding for Categorical and Crossed Lie Algebras and Simplicial Lie Algebras”, Turkish Journal of Math., 31, 2007, pp. 239-255.
  • A. Fernández-Fariña, and M. Ladra, “Braiding for categorical algebras and crossed modules of algebras I: Associative and Lie algebras”, Journal of Algebra and Its Applications, 19 (09), 2020, 2050176, 24 pages.
  • E. Iğde, and K. Yılmaz, “Tensor products and crossed differential graded Lie algebras in the category of crossed complexes”. Symmetry, 2023, 15(9), 1646.
  • M. Alp, “Characterization of crossed corner”, Algebras, Groups and Geometries, 16(2), 1999, pp. 173–182.
  • M. Alp, “Applications of crossed corner”, Algebras, Groups and Geometries, 16(2), 1999, pp. 337–344.
  • M. Alp, A. Bekir, and E. Ulualan, “Relation between crossed square and crossed corner”, Journal of Science and Technology of Dumlupınar University, 2001, (002), pp. 89-96.
  • Ö. Gürmen Alansal, “Crossed corner and reduced simplicial commutative algebras”. Journal of New Theory, (45), 2023, pp. 95-104.
  • H. Binbir, and Ö. Gürmen Alansal, “Değişmeli Cebirler için Çaprazlanmış Köşe ve Moore Bikompleks”. Kırşehir Ahi Evran Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2(1), 2024, pp. 12-18.
  • I. Kurtuluş, “Lie Cebirleri için Çaprazlanmış Köşe ve İlişkili Yapılar”. M.S. thesis, Institute of Graduate Education, Kütahya Dumlupınar University., Kütahya., Türkiye, 2025.
  • M. Artin, and B. Mazur, “On the Van Kampen Theorem”, Topology, 5, 1966, pp. 179-189.
  • Z. Arvasi, M. Koçak, and E. Ulualan, “Braided crossed modules and reduced simplicial groups”. Taiwanese Journal of Mathematics. 9(3), 2005, pp. 477-488.
  • J. M. Casas. “Crossed extensions of Leibniz algebras”. Communications in Algebra, 27(12), 1999, pp. 6253-6272.
  • J. M. Casas, M. Ladra, T. Pirashvili, “Crossed modules for Lie-Rinehart algebras”. Cent. Eur. Journal of Algebra, 274(1), 2004, pp. 192-201.
  • A. Aytekin, “Categorical structures of Lie-Rinehart crossed module”. Turkish Journal of Math., 43(1), 2019, pp. 511-522.
  • M. Koçak, and S. Çetin, “Higher Dimensional Leibniz-Rinehart Algebras”. Journal of Mathematical Sciences and Modelling, 7(1), 2024, pp. 45-50.

Lie Cebirlerinde Çaprazlanmış köşe

Yıl 2025, Cilt: 14 Sayı: 2, 877 - 886, 30.06.2025

Işıl Zekiye Kurtuluş Özgün Gürmen Alansal

https://doi.org/10.17798/bitlisfen.1606755

Öz

Bu çalışmada, lie cebirlerinde çapraz köşeyi tanımlıyoruz ve lie cebirlerinde çapraz köşe kategorisi ile Moore kompleksinin uzunluğu 2 olan indirgenmiş simplisel lie cebirleri kategorisi arasındaki denkliği oluşturuyoruz.

Anahtar Kelimeler

lie cebir çaprazlanmış modül çaprazlanmış köşe

Kaynakça

  • J. H. C. Whitehead, “Combinatorial Homotopy II”, Bulletin of the American Mathematical Society, 55, 1949, pp. 453-496.
  • C. Kassel, and J. L. Loday, “Extensions Centrales D’algébres de Lie”, Annales de l’institut Fourier, 33,1982, pp.119-142.
  • G. J. Ellis, “Higher Dimensional Crossed Modules of Algebras”, Journal of Pure and Applied Algebra, 52, 1988, pp. 277-282.
  • I. I. Akça, and Z. Arvasi, “Simplicial and Crossed Lie Algebras, Homology”, Homotopy and Applications, 4 (1), 2002, pp. 43-57.
  • E. Ulualan, and E. Uslu, “Quadratic Modules for Lie Algebras”, Hacettepe Journal of Mathematics and Statistics, 40 (3), 2011, pp. 409-419.
  • E. Özel, and U. E. Arslan, “On Quasi Quadratic Modules of Lie Algebras”, Journal of New Theory, (41), 2022, pp. 62-69.
  • E. Ulualan, “Braiding for Categorical and Crossed Lie Algebras and Simplicial Lie Algebras”, Turkish Journal of Math., 31, 2007, pp. 239-255.
  • A. Fernández-Fariña, and M. Ladra, “Braiding for categorical algebras and crossed modules of algebras I: Associative and Lie algebras”, Journal of Algebra and Its Applications, 19 (09), 2020, 2050176, 24 pages.
  • E. Iğde, and K. Yılmaz, “Tensor products and crossed differential graded Lie algebras in the category of crossed complexes”. Symmetry, 2023, 15(9), 1646.
  • M. Alp, “Characterization of crossed corner”, Algebras, Groups and Geometries, 16(2), 1999, pp. 173–182.
  • M. Alp, “Applications of crossed corner”, Algebras, Groups and Geometries, 16(2), 1999, pp. 337–344.
  • M. Alp, A. Bekir, and E. Ulualan, “Relation between crossed square and crossed corner”, Journal of Science and Technology of Dumlupınar University, 2001, (002), pp. 89-96.
  • Ö. Gürmen Alansal, “Crossed corner and reduced simplicial commutative algebras”. Journal of New Theory, (45), 2023, pp. 95-104.
  • H. Binbir, and Ö. Gürmen Alansal, “Değişmeli Cebirler için Çaprazlanmış Köşe ve Moore Bikompleks”. Kırşehir Ahi Evran Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2(1), 2024, pp. 12-18.
  • I. Kurtuluş, “Lie Cebirleri için Çaprazlanmış Köşe ve İlişkili Yapılar”. M.S. thesis, Institute of Graduate Education, Kütahya Dumlupınar University., Kütahya., Türkiye, 2025.
  • M. Artin, and B. Mazur, “On the Van Kampen Theorem”, Topology, 5, 1966, pp. 179-189.
  • Z. Arvasi, M. Koçak, and E. Ulualan, “Braided crossed modules and reduced simplicial groups”. Taiwanese Journal of Mathematics. 9(3), 2005, pp. 477-488.
  • J. M. Casas. “Crossed extensions of Leibniz algebras”. Communications in Algebra, 27(12), 1999, pp. 6253-6272.
  • J. M. Casas, M. Ladra, T. Pirashvili, “Crossed modules for Lie-Rinehart algebras”. Cent. Eur. Journal of Algebra, 274(1), 2004, pp. 192-201.
  • A. Aytekin, “Categorical structures of Lie-Rinehart crossed module”. Turkish Journal of Math., 43(1), 2019, pp. 511-522.
  • M. Koçak, and S. Çetin, “Higher Dimensional Leibniz-Rinehart Algebras”. Journal of Mathematical Sciences and Modelling, 7(1), 2024, pp. 45-50.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebir ve Sayı Teorisi, Kategori Teorisi, K Teorisi, Homolojik Cebir
Bölüm Research Article
Yazarlar

Işıl Zekiye Kurtuluş 0000-0002-6721-9416

Özgün Gürmen Alansal 0000-0003-2851-986X

Erken Görünüm Tarihi 27 Haziran 2025
Yayımlanma Tarihi 30 Haziran 2025
Gönderilme Tarihi 24 Aralık 2024
Kabul Tarihi 24 Haziran 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 14 Sayı: 2

Kaynak Göster

IEEE I. Z. Kurtuluş ve Ö. Gürmen Alansal, “Crossed Corner of Lie Algebras”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, c. 14, sy. 2, ss. 877–886, 2025, doi: 10.17798/bitlisfen.1606755.
 Kapak Resmi İndir

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS