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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Volume: 49 Issue: 6

Higher dimensional algebras as ideal maps

Alper Odabas(ESKISEHIR OSMANGAZI UNIVERSITY, FACULTY OF SCIENCE AND LETTERS)0000-0002-4361-3056
Erdal Ulualan(DUMLUPINAR UNIVERSITY)0000-0002-4823-8267
Sayfa
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Yayın Tarihi
2020-12-08
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We also explain this structure for crossed squares of algebras.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this work, we explain the close relationship between an ideal map structure $S\rightarrow End_{R}(R)$ on a homomorphism of commutative $k$-algebras $R\rightarrow S$ and an ideal simplicial algebra structure on the associated bar construction $Bar(S,R)$.
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Temel Bulgular & Veri:In this work, we explain the close relationship between an ideal map structure $S\rightarrow End_{R}(R)$ on a homomorphism of commutative $k$-algebras $R\rightarrow S$ and an ideal simplicial algebra structure on the associated bar construction $Bar(S,R)$.
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Sonuç & Katkı:We also explain this structure for crossed squares of algebras.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:crossed module · crossed square · ideal map

Abstract

In this work, we explain the close relationship between an ideal map structure $S\rightarrow End_{R}(R)$ on a homomorphism of commutative $k$-algebras $R\rightarrow S$ and an ideal simplicial algebra structure on the associated bar construction $Bar(S,R)$. We also explain this structure for crossed squares of algebras.

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Bu Makaleye Atıf Yap

Odabas, A., Ulualan, E. (2020). Higher dimensional algebras as ideal maps. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 6. https://doi.org/10.15672/hujms.575080

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Kaynakça (16)

  1. M. André, Homologie des algèbres commutatives, Die Grundlehren der Mathematischen Wissenchaften, 206 Springer-Verlag 1974.
  2. Z. Arvasi and T. Porter, Higher dimensional Peiffer elements in simplicial commutative algebras, Theory Appl. Categ., 3, No. 1, pp 1-23, 1997.
  3. Z. Arvasi and T. Porter, Freeness conditions for 2-crossed module of commutative algebras, Appl. Categ. Structures, 6, 455-471, 1998.
  4. Z. Arvasi and A. Odabaş, Computing 2-dimensional algebras: Crossed modules and Cat1-algebras, J. Algebra Appl. 15 (10), 1650185, 2016.
  5. T. Datuashvili and T. Pirashvili, On Co Homology of 2-Types and Crossed Modules, J. Algebra 244, 352-365, 2001.
  6. G. Ellis, Higher dimensional crossed modules of algebras, J. Pure Appl. Algebra 52, 277-282, 1988.
  7. G. Ellis, Crossed squares and combinatorial homotopy, Math. Z. 214, 93-110, 1993.
  8. E.D. Farjoun and K. Hess, Normal and co-normal maps in homotopy theory, Homology Homotopy Appl. 14, 1, 79-112, 2012.
  9. E.D. Farjoun and Y. Segev, Crossed modules as homotopy normal maps, Topology Appl. 157, 359-368, 2010.
  10. E.D. Farjoun and Y. Segev, Normal closure and injective normalizer of a group homomorphism, J. Algebra 423, 1010-1043, 2015.
  11. D. Guin-Waléry and J-L. Loday, Obsructioná l’excision en K-theories algébrique, In: Friedlander, E.M.,Stein, M.R.(eds.) Evanston conf. on algebraic K-Theory 1980, (Lecture Notes in Math., 854, 179-216), Springer, Berlin Heidelberg, 1981.
  12. L. Illusie, Complex cotangent et deformations I, II, Lecture Notes in Math. 239 1971, II: 283, Springer, 1972.
  13. T. Porter, Homology of commutative algebras and an invariant of Simis and Vasconceles, J. Algebra 99, 458-465, 1986.
  14. M. Prezma, Homotopy normal maps, Algebr. Geom. Topol. 12, 1211-1238, 2012.
  15. N.M. Shammu, Algebraic and categorical structure of category of crossed modules of algebras, University of Wales, PhD Thesis, 1992.
  16. J.H.C. Whitehead, Combinatorial homotopy II, Bull. Amer. Math. Soc. 55, 453-496, 1949.