Outcome for the case (11,10; 1)

Authors

  • Waleed Khalid Jaber Department of Mathematics, College of Education for Pure Science Ibn-Al-Haitham, University of Baghdad, Baghdad, Iraq. & Department of Mathematics, College of Computer Sciences and Mathematics, University of Thi-Qar, Nassiriyah, Iraq https://orcid.org/0000-0002-3998-6861
  • Niran Sabah Jasim Department of Mathematics, College of Education for pure Science Ibn-Al-Haitham, University of Baghdad, Baghdad, Iraq.

DOI:

https://doi.org/10.21123/bsj.2024.9905

Keywords:

Divided power algebra, Letter place, Overlap, Place polarizations, Resolution, Weyl module.

Abstract

Through this work R is a commutative ring with 1,  is a free R-module and  is the divided power algebra of degree . A partition of length ℓ(l) = n is a sequence  = (l1, l2, …, ln) of non-negative integers in non-increasing order l1³ l2 ³  …³ ln > 0. The weight of a partition l is ÷l÷ = l1 + l2 + …+ ln. A relative sequence is a pair  of sequences such that   m £ l and denoted by . If both  and  are partitions then the relative sequence   is called a skew partition. Let  be the free generator of divided power algebra  in one generator. The divided power element  of degree  of the free generator  acts on  by place polarization of degree    from place 1 to place 2. The graded algebra  acts on the graded module , the degree of the second factor determines the grading.  M is a graded left odule, where for   and , so we have: . This article surveys the exactness of the Weyl resolution of the sequence for the case (11,10; 1) after getting the contracting homotopy of { }; where  = 0,1, …, 8, and the terms of the characteristic-free resolution for it.

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Outcome for the case (11,10; 1). Baghdad Sci.J [Internet]. [cited 2024 Oct. 9];22(4). Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/9905