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Module Structure of Generalized Weyl Algebra

Ansari, Khursed
http://rave.ohiolink.edu/etdc/view?acc_num=toledo1627979620104427

Abstract Details

2021, Doctor of Philosophy, University of Toledo, Mathematics.
Define the generalized Weyl algebra An,f (K) of degree n, over K to be an algebraically closed field of characteristic zero, with identity, generated by the 3n indeterminates x1, x2, ..., xn, y1, y2, ..., yn, z1, z2, ..., zn subject to the relations xi xj – xj xi = yi yj – yj yi = zi zj – zj zi = 0, [xi , yi ] = yi , [xi , zi ] = − zi , yi zi = fi(xi), zi yi = fi(xi + 1), xi yj – yj xi = xi zj – zj xi = yi zj – zj yi = 0 and f = (f1, ..., fn) and each fi is a polynomial. J.T. Stafford [2] has proved that every left(right) ideal in Weyl algebra can be generated by two elements. The goal of this thesis is to show that the same result holds for An,f (K). The idea of proof is similar to that of Weyl algebra case given on [1]. This part of proof is presented in Chapter 3.
Alimjon Eshmatov (Advisor)
Ryad Ghanam (Committee Member)
Ekaterina Shemyakova (Committee Member)
Gerard Thompson (Committee Member)
49 p.
Mathematics

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Citations

  • Ansari, K. (2021). Module Structure of Generalized Weyl Algebra [Doctoral dissertation, University of Toledo]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1627979620104427

    APA Style (7th edition)

  • Ansari, Khursed. Module Structure of Generalized Weyl Algebra. 2021. University of Toledo, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=toledo1627979620104427.

    MLA Style (8th edition)

  • Ansari, Khursed. "Module Structure of Generalized Weyl Algebra." Doctoral dissertation, University of Toledo, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1627979620104427

    Chicago Manual of Style (17th edition)

toledo1627979620104427
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© 2021, some rights reserved.Creative Commons License Module Structure of Generalized Weyl Algebra by Khursed Ansari is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Toledo and OhioLINK.
Release 3.2.12