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Year 2022, Volume: 11 Issue: 3, 210 - 221, 31.12.2022
https://doi.org/10.54187/jnrs.1184962
https://izlik.org/JA64LP22JW

Abstract

References

  • J. H. C. Whitehead, Combinatorial homotopy. II, Bulletin of the American Mathematical Society, 55(5), (1949) 453-496.
  • M. Gerstenhaber, On the deformation of rings and algebras, Annals of Mathematics Second Series, 79(1) (1964) 59-103.
  • S. Lichtenbaum, M. Schlessinger, The cotangent complex of a morphism, Transactions of the American Mathematical Society, 128(1), (1967) 41-70.
  • T. Porter, Some categorical results in the theory of crossed modules in commutative algebras, Journal of Algebra, 109(2), (1987) 415-429.
  • P. Dedecker, A. S-T. Lue, A nonabelian two-dimensional cohomology for associative algebras, Bulletin of the American Mathematical Society, 72(6), (1966) 1044-1050.
  • Z. Arvasi, U. E. Arslan, Annihilators, multipliers and crossed modules, Applied Categorical Structures, 11(6), (2003) 487-506.
  • U. E. Arslan, İ. İ. Akça, G. I. Onarlı, O. Avcıoğlu, Fibrations of 2-crossed modules, Mathematical Methods in the Applied Sciences, 42(16), (2019) 5293-5304.
  • U. E. Arslan, Serdar Hürmetli, Bimultiplications and annihilators of crossed modules in associative algebras, Journal of New Theory, (35), (2021) 72-90.
  • A. Aytekin, Categorical structures of Lie-Rinehart crossed module, Turkish Journal of Mathematics, 43(1), (2019) 511-522.
  • C. Kassel, J. L. Loday, Extensions centrales d'alg\'ebres de Lie, Annales de l'Institut Fourier (Grenoble), 32(4), (1982) 119-142.
  • J. M. Casas, M. Ladra, Colimits in the crossed modules category in Lie algebras, Georgian Mathematical Journal, 7(3), (2000) 461-474.
  • G. J. Ellis, Homotopical aspects of Lie algebras, Journal of the Australian Mathematical Society (Series A), 54(3), (1993) 393-419.
  • D. Conduch\'e, Modules Crois\'es G\'en\'eralis\'es de Longueur 2, Journal of Pure and Applied Algebra, 34(2-3), (1984) 155-178.
  • J. F. Martins, The fundamental 2-crossed complex of a reduced CW-complex, Homology, Homotopy and Applications, 13(2), (2011) 129-157.
  • B. Gohla, J. F. Martins, Pointed homotopy and pointed lax homotopy of 2-crossed module maps, Advances in Mathematics, 248, (2013) 986-1049.
  • İ. Akça, K. Emir, J. F. Martins, Pointed homotopy of 2-crossed module maps on commutative algebras, Homology, Homotopy and Applications, 18(1), (2016) 99-128.
  • P. Carrasco, T. Porter, Coproduct of 2-crossed modules: Applications to a definition of a tensor product for 2-crossed complexes, Collectanea Mathematica, 3(67), (2016) 485-517.
  • R. Brown, N. D. Gilbert, Algebraic models of 3-types and automorphism structures for crossed modules, Proceedings of the London Mathematical Society, (3)59, (1989) 51-73.
  • J. L. Loday, Space with finitely many non-trivial homotopy groups, Journal of Pure and Applied Algebra, 24(2), (1982) 179-202.
  • Z. Arvasi, Crossed squares and 2-crossed modules of commutative algebras, Theory and Applications of Categories, 3(7), (1997) 160-181.
  • Z. Arvasi, T. Porter, Freeness conditions for 2-crossed modules of commutative algebras, Applied Categorical Structure, 6(4), (1998) 455-471.
  • H. J. Baues, Combinatorial homotopy and 4-dimensional complexes, Walter de Gruyter, Berlin, 1991.
  • E. Ulualan, E. Uslu, Quadratic modules for Lie algebras, Hacettepe Journal of Mathematics and Statistics, 40(3), (2011) 409-419.
  • A. Odabaş, E Ulualan, On free quadratic modules of commutative algebras, Bulletin of the Malaysian Mathematical Sciences Society, 39(3), (2016) 1059-1074.
  • K. Yılmaz, E. S. Yılmaz, Baues cofibration for quadratic modules of Lie algebras, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), (2019) 1653-1663.
  • E. Özel, Pointed homotopy theory of quadratic modules of Lie algebras, Master's Thesis, Eskişehir Osmangazi University (2017) Eskişehir, Türkiye (in Turkish).
  • U. E. Arslan, E. Özel, On homotopy theory of quadratic modules of Lie algebras, Konuralp Journal of Mathematics, 10(1), (2022) 159-165.
  • R. Brown, P. J. Higgins, R. Sivera, Nonabelian Algebraic Topology: Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids, Tracts in Mathematics, European Mathematical Society, 2010.
  • E. Özel, U. E. Arslan, On quasi quadratic modules of Lie algebras, Journal of New Theory(41), (2022) 62-69.

Finite coproducts in the category of quadratic modules of Lie algebras

Year 2022, Volume: 11 Issue: 3, 210 - 221, 31.12.2022
https://doi.org/10.54187/jnrs.1184962
https://izlik.org/JA64LP22JW

Abstract

In this study, we will construct finite coproduct objects in the category of quadratic modules of Lie algebras with a new approach using the idea of quasi-quadratic modules.

References

  • J. H. C. Whitehead, Combinatorial homotopy. II, Bulletin of the American Mathematical Society, 55(5), (1949) 453-496.
  • M. Gerstenhaber, On the deformation of rings and algebras, Annals of Mathematics Second Series, 79(1) (1964) 59-103.
  • S. Lichtenbaum, M. Schlessinger, The cotangent complex of a morphism, Transactions of the American Mathematical Society, 128(1), (1967) 41-70.
  • T. Porter, Some categorical results in the theory of crossed modules in commutative algebras, Journal of Algebra, 109(2), (1987) 415-429.
  • P. Dedecker, A. S-T. Lue, A nonabelian two-dimensional cohomology for associative algebras, Bulletin of the American Mathematical Society, 72(6), (1966) 1044-1050.
  • Z. Arvasi, U. E. Arslan, Annihilators, multipliers and crossed modules, Applied Categorical Structures, 11(6), (2003) 487-506.
  • U. E. Arslan, İ. İ. Akça, G. I. Onarlı, O. Avcıoğlu, Fibrations of 2-crossed modules, Mathematical Methods in the Applied Sciences, 42(16), (2019) 5293-5304.
  • U. E. Arslan, Serdar Hürmetli, Bimultiplications and annihilators of crossed modules in associative algebras, Journal of New Theory, (35), (2021) 72-90.
  • A. Aytekin, Categorical structures of Lie-Rinehart crossed module, Turkish Journal of Mathematics, 43(1), (2019) 511-522.
  • C. Kassel, J. L. Loday, Extensions centrales d'alg\'ebres de Lie, Annales de l'Institut Fourier (Grenoble), 32(4), (1982) 119-142.
  • J. M. Casas, M. Ladra, Colimits in the crossed modules category in Lie algebras, Georgian Mathematical Journal, 7(3), (2000) 461-474.
  • G. J. Ellis, Homotopical aspects of Lie algebras, Journal of the Australian Mathematical Society (Series A), 54(3), (1993) 393-419.
  • D. Conduch\'e, Modules Crois\'es G\'en\'eralis\'es de Longueur 2, Journal of Pure and Applied Algebra, 34(2-3), (1984) 155-178.
  • J. F. Martins, The fundamental 2-crossed complex of a reduced CW-complex, Homology, Homotopy and Applications, 13(2), (2011) 129-157.
  • B. Gohla, J. F. Martins, Pointed homotopy and pointed lax homotopy of 2-crossed module maps, Advances in Mathematics, 248, (2013) 986-1049.
  • İ. Akça, K. Emir, J. F. Martins, Pointed homotopy of 2-crossed module maps on commutative algebras, Homology, Homotopy and Applications, 18(1), (2016) 99-128.
  • P. Carrasco, T. Porter, Coproduct of 2-crossed modules: Applications to a definition of a tensor product for 2-crossed complexes, Collectanea Mathematica, 3(67), (2016) 485-517.
  • R. Brown, N. D. Gilbert, Algebraic models of 3-types and automorphism structures for crossed modules, Proceedings of the London Mathematical Society, (3)59, (1989) 51-73.
  • J. L. Loday, Space with finitely many non-trivial homotopy groups, Journal of Pure and Applied Algebra, 24(2), (1982) 179-202.
  • Z. Arvasi, Crossed squares and 2-crossed modules of commutative algebras, Theory and Applications of Categories, 3(7), (1997) 160-181.
  • Z. Arvasi, T. Porter, Freeness conditions for 2-crossed modules of commutative algebras, Applied Categorical Structure, 6(4), (1998) 455-471.
  • H. J. Baues, Combinatorial homotopy and 4-dimensional complexes, Walter de Gruyter, Berlin, 1991.
  • E. Ulualan, E. Uslu, Quadratic modules for Lie algebras, Hacettepe Journal of Mathematics and Statistics, 40(3), (2011) 409-419.
  • A. Odabaş, E Ulualan, On free quadratic modules of commutative algebras, Bulletin of the Malaysian Mathematical Sciences Society, 39(3), (2016) 1059-1074.
  • K. Yılmaz, E. S. Yılmaz, Baues cofibration for quadratic modules of Lie algebras, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), (2019) 1653-1663.
  • E. Özel, Pointed homotopy theory of quadratic modules of Lie algebras, Master's Thesis, Eskişehir Osmangazi University (2017) Eskişehir, Türkiye (in Turkish).
  • U. E. Arslan, E. Özel, On homotopy theory of quadratic modules of Lie algebras, Konuralp Journal of Mathematics, 10(1), (2022) 159-165.
  • R. Brown, P. J. Higgins, R. Sivera, Nonabelian Algebraic Topology: Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids, Tracts in Mathematics, European Mathematical Society, 2010.
  • E. Özel, U. E. Arslan, On quasi quadratic modules of Lie algebras, Journal of New Theory(41), (2022) 62-69.
There are 29 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Emre Özel 0000-0002-5106-443X

Ummahan Ege Arslan 0000-0002-2995-0718

İbrahim İlker Akça 0000-0003-4269-498X

Publication Date December 31, 2022
DOI https://doi.org/10.54187/jnrs.1184962
IZ https://izlik.org/JA64LP22JW
Published in Issue Year 2022 Volume: 11 Issue: 3

Cite

APA Özel, E., Ege Arslan, U., & Akça, İ. İ. (2022). Finite coproducts in the category of quadratic modules of Lie algebras. Journal of New Results in Science, 11(3), 210-221. https://doi.org/10.54187/jnrs.1184962
AMA 1.Özel E, Ege Arslan U, Akça İİ. Finite coproducts in the category of quadratic modules of Lie algebras. JNRS. 2022;11(3):210-221. doi:10.54187/jnrs.1184962
Chicago Özel, Emre, Ummahan Ege Arslan, and İbrahim İlker Akça. 2022. “Finite Coproducts in the Category of Quadratic Modules of Lie Algebras”. Journal of New Results in Science 11 (3): 210-21. https://doi.org/10.54187/jnrs.1184962.
EndNote Özel E, Ege Arslan U, Akça İİ (December 1, 2022) Finite coproducts in the category of quadratic modules of Lie algebras. Journal of New Results in Science 11 3 210–221.
IEEE [1]E. Özel, U. Ege Arslan, and İ. İ. Akça, “Finite coproducts in the category of quadratic modules of Lie algebras”, JNRS, vol. 11, no. 3, pp. 210–221, Dec. 2022, doi: 10.54187/jnrs.1184962.
ISNAD Özel, Emre - Ege Arslan, Ummahan - Akça, İbrahim İlker. “Finite Coproducts in the Category of Quadratic Modules of Lie Algebras”. Journal of New Results in Science 11/3 (December 1, 2022): 210-221. https://doi.org/10.54187/jnrs.1184962.
JAMA 1.Özel E, Ege Arslan U, Akça İİ. Finite coproducts in the category of quadratic modules of Lie algebras. JNRS. 2022;11:210–221.
MLA Özel, Emre, et al. “Finite Coproducts in the Category of Quadratic Modules of Lie Algebras”. Journal of New Results in Science, vol. 11, no. 3, Dec. 2022, pp. 210-21, doi:10.54187/jnrs.1184962.
Vancouver 1.Emre Özel, Ummahan Ege Arslan, İbrahim İlker Akça. Finite coproducts in the category of quadratic modules of Lie algebras. JNRS. 2022 Dec. 1;11(3):210-21. doi:10.54187/jnrs.1184962

 

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