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Characteristic 0 Resolution of the Weyl Module in the Event of Partitioning (4, 4, 3) | ||
| Journal of University of Anbar for Pure Science | ||
| Article 38, Volume 17, Issue 2, December 2023, Pages 311-316 PDF (625.77 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.37652/juaps.2023.141652.1094 | ||
| Authors | ||
| Haytham Razooki Hassan* 1; Hayder Muhi Hashim* 2 | ||
| 1Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq | ||
| 2Ministry of Education, General Directorate of Education of Babylon, Babylon, Iraq | ||
| Abstract | ||
| Let R be a commutative ring with 1, Ӻ be a free R-module and Ḍ_į be "the divided power algebra" of degree į. Ṃ is a left-graded module with for Ѡ = Ƶ_21^ҝ⋵ Å and Ѵ ⋵〖 Ḍ〗_(ᴯ_1 )⊗ Ḍ_(ᴯ_2 ) .Consequently, we have Ѡ(Ѵ)= Ƶ_(21 )^ҝ (Ѵ)=〖 ∂〗_(21 )^ҝ (Ѵ). where the separator ẋ vanishes between Ƶ_ḁᵬ^((ț))and ∂_ḁᵬ^((ț)). We depend on the definition of the mapping Cone and applying that for the partition (4, 4, 3) to find the resolution of the Weyl module for characteristic 0 "in the situation of partition (4, 4, 3) without depends on the resolution of the Weyl module for characteristic free". Also by using Capelli identities we prove the sequences and the subsequences of the terms of characteristic zero satisfy the mapping Cone. Finally by the commutative of each diagram in these sequences and subsequences we get the reduction of the terms of the resolution of the Weyl module for characteristic free to the terms of the resolution of the Weyl module for characteristic 0. | ||
| Keywords | ||
| Mapping Cone,,; ,،Divided Power Algebra,,; ,،Place Polarization,,; ,،Resolution of Weyl Module | ||
| References | ||
|
[1].Haytham R.H. 2013 Complex of Lascoux in Partition (4,4,4), Iraqi Journal of Science, Vol. 54,No. 1, pp. 170-173.
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[3].Haytham R.H., Niran S.J. 2018 A Complex of Characteristic Zero in the Case of the Partition (8,7,3), Science International (Lahore), Vol. 30, No. 4, pp.639-641.
[4].Haytham R.H., Niran S.J. 2018 Application of Weyl Module in the Case of Two Rows, J. Phys.:Conf.Ser., Vol. 1003 (012051), pp.1-15 .
[5].Haytham R.H., Niran S.J. 2018 On Free Resolution of Weyl Module and Zero Characteristic Resolution In The Case of Partition (8,7,3), Baghdad Science Journal, Vol. 15, No. 4, pp. 455-465 .
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[7].Vermani, L.R. 2003 An elementary approach to homogical algebra, Chapman and Hall/CRC, Monographs and Surveys in pure and Applied mathematics, Vol.130 . | ||
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