Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2023, , 177 - 187, 30.09.2023

Özgün Gürmen Alansal , Erdal Ulualan

https://doi.org/10.33401/fujma.1292885
Cited By: 2

Öz

Kaynakça

  • [1] A.R. Grandjean, M.J. Vale, 2-Modulos cruzados an la cohomologia de andr´e-quillen, Memorias de la Real Academia de Ciencias, 22 (1986), 1–28.
  • [2] D. Conduche, Modules crois´es c´en´eralis´es de longueur 2, J. Pure Appl. Algebra, 34 (1984), 155-178.
  • [3] D. Conduche, Simplicial crossed modules and mapping cones, Georgian Math. J., 10(4) (2003), 623-636.
  • [4] D. Guin-Wal´ery, J-L. Loday, Obsruction´a l’excision en K-theories Alg´ebrique, Evanston conference on Algebraic K-Theory 1980, (Lectute Notes Mathematics) 854, 179-216, Berlin Heidelberg New York, Springer 1981.
  • [5] G.J. Ellis, Higher dimensional crossed modules of algebras, J. Pure Appl. Algebra, 52 (1988), 277-282.
  • [6] J.H.C. Whitehead, Combinatorial homotopy II, Bull. Amer. Math. Soc., 55 (1949), 453-496.
  • [7] L. Illusie, Complex Cotangent et Deformations I, II, Springer Lecture Notes in Mathematics 239 1971 II 283 1972.
  • [8] M. Andre, Homologie des Algebres Commutatives, Die Grundlehren der Mathematischen Wissenchaften, 206 New York, Springer-Verlag, 1974.
  • [9] Ö. Gürmen Alansal, E. Ulualan, Peiffer pairings in multisimplicial groups and crossed n-cubes and applications for bisimplicial groups, Turkish J. Math., 45(1) (2021), 360-386.
  • [10] P. Carrasco, A.M. Cegarra, Group-theoretic algebraic models for homotopy types, J. Pure Appl. Algebra, 75 (1991), 19-235.
  • [11] T. Porter, Homology of commutative algebras and an invariant of simis and vasconceles, J. Algebr., 99 (1986), 458-465.
  • [12] T. Porter, n-type of simplicial groups and crossed n-cubes, Topol., 32 (1993), 5-24.
  • [13] Z. Arvasi, T. Porter, Higher dimensional Peiffer elements in simplicial commutative algebras, Theory Appl. Categ., 3(1) (1997), 1-23.
  • [14] Z. Arvasi, Crossed squares and 2-crossed modules of commutative algebras, Theory Appl. Categ., 3(7) (1997), 160-181.

Bisimplicial Commutative Algebras and Crossed Squares

Yıl 2023, , 177 - 187, 30.09.2023

Özgün Gürmen Alansal , Erdal Ulualan

https://doi.org/10.33401/fujma.1292885
Cited By: 2

Öz

A simplicial commutative algebra with Moore complex of length 1 gives a crossed module structure over commutative algebras. In this study, we will give 2-dimensional version of this result by giving hypercrossed complex pairings for a bisimplicial algebra and its Moore bicomplex. We give a detailed calculation in low dimensions for these pairings to see their role in the structures of crossed squares and bisimplicial algebras. In this context, we prove that if the Moore bicomplex of a bisimplicial commutative algebra is of length 1, then it gives a crossed square structure over commutative algebras.

Anahtar Kelimeler

Bisimplicial algebras Crossed modules Moore complex

Kaynakça

  • [1] A.R. Grandjean, M.J. Vale, 2-Modulos cruzados an la cohomologia de andr´e-quillen, Memorias de la Real Academia de Ciencias, 22 (1986), 1–28.
  • [2] D. Conduche, Modules crois´es c´en´eralis´es de longueur 2, J. Pure Appl. Algebra, 34 (1984), 155-178.
  • [3] D. Conduche, Simplicial crossed modules and mapping cones, Georgian Math. J., 10(4) (2003), 623-636.
  • [4] D. Guin-Wal´ery, J-L. Loday, Obsruction´a l’excision en K-theories Alg´ebrique, Evanston conference on Algebraic K-Theory 1980, (Lectute Notes Mathematics) 854, 179-216, Berlin Heidelberg New York, Springer 1981.
  • [5] G.J. Ellis, Higher dimensional crossed modules of algebras, J. Pure Appl. Algebra, 52 (1988), 277-282.
  • [6] J.H.C. Whitehead, Combinatorial homotopy II, Bull. Amer. Math. Soc., 55 (1949), 453-496.
  • [7] L. Illusie, Complex Cotangent et Deformations I, II, Springer Lecture Notes in Mathematics 239 1971 II 283 1972.
  • [8] M. Andre, Homologie des Algebres Commutatives, Die Grundlehren der Mathematischen Wissenchaften, 206 New York, Springer-Verlag, 1974.
  • [9] Ö. Gürmen Alansal, E. Ulualan, Peiffer pairings in multisimplicial groups and crossed n-cubes and applications for bisimplicial groups, Turkish J. Math., 45(1) (2021), 360-386.
  • [10] P. Carrasco, A.M. Cegarra, Group-theoretic algebraic models for homotopy types, J. Pure Appl. Algebra, 75 (1991), 19-235.
  • [11] T. Porter, Homology of commutative algebras and an invariant of simis and vasconceles, J. Algebr., 99 (1986), 458-465.
  • [12] T. Porter, n-type of simplicial groups and crossed n-cubes, Topol., 32 (1993), 5-24.
  • [13] Z. Arvasi, T. Porter, Higher dimensional Peiffer elements in simplicial commutative algebras, Theory Appl. Categ., 3(1) (1997), 1-23.
  • [14] Z. Arvasi, Crossed squares and 2-crossed modules of commutative algebras, Theory Appl. Categ., 3(7) (1997), 160-181.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Özgün Gürmen Alansal 0000-0003-2851-986X

Erdal Ulualan 0000-0002-4823-8267

Yayımlanma Tarihi 30 Eylül 2023
Gönderilme Tarihi 5 Mayıs 2023
Kabul Tarihi 22 Eylül 2023
Yayımlandığı Sayı Yıl 2023

Kaynak Göster

APA Gürmen Alansal, Ö., & Ulualan, E. (2023). Bisimplicial Commutative Algebras and Crossed Squares. Fundamental Journal of Mathematics and Applications, 6(3), 177-187. https://doi.org/10.33401/fujma.1292885
AMA Gürmen Alansal Ö, Ulualan E. Bisimplicial Commutative Algebras and Crossed Squares. Fundam. J. Math. Appl. Eylül 2023;6(3):177-187. doi:10.33401/fujma.1292885
Chicago Gürmen Alansal, Özgün, ve Erdal Ulualan. “Bisimplicial Commutative Algebras and Crossed Squares”. Fundamental Journal of Mathematics and Applications 6, sy. 3 (Eylül 2023): 177-87. https://doi.org/10.33401/fujma.1292885.
EndNote Gürmen Alansal Ö, Ulualan E (01 Eylül 2023) Bisimplicial Commutative Algebras and Crossed Squares. Fundamental Journal of Mathematics and Applications 6 3 177–187.
IEEE Ö. Gürmen Alansal ve E. Ulualan, “Bisimplicial Commutative Algebras and Crossed Squares”, Fundam. J. Math. Appl., c. 6, sy. 3, ss. 177–187, 2023, doi: 10.33401/fujma.1292885.
ISNAD Gürmen Alansal, Özgün - Ulualan, Erdal. “Bisimplicial Commutative Algebras and Crossed Squares”. Fundamental Journal of Mathematics and Applications 6/3 (Eylül 2023), 177-187. https://doi.org/10.33401/fujma.1292885.
JAMA Gürmen Alansal Ö, Ulualan E. Bisimplicial Commutative Algebras and Crossed Squares. Fundam. J. Math. Appl. 2023;6:177–187.
MLA Gürmen Alansal, Özgün ve Erdal Ulualan. “Bisimplicial Commutative Algebras and Crossed Squares”. Fundamental Journal of Mathematics and Applications, c. 6, sy. 3, 2023, ss. 177-8, doi:10.33401/fujma.1292885.
Vancouver Gürmen Alansal Ö, Ulualan E. Bisimplicial Commutative Algebras and Crossed Squares. Fundam. J. Math. Appl. 2023;6(3):177-8.

Cited By

Whiskered Groupoids and Crossed Modules with Diagrams
Journal of New Theory
https://doi.org/10.53570/jnt.1403803
Crossed Corner and Reduced Simplicial Commutative Algebras
Journal of New Theory
https://doi.org/10.53570/jnt.1391397

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