Integral Basis Theorem of cyclotomic Khovanov-Lauda-Rouquier Algebras of type A
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Type
ThesisThesis type
Doctor of PhilosophyAuthor/s
Li, Ge JrAbstract
The main purpose of this thesis is to prove that the cyclotomic Khovanov-Lauda-Rouquier algebras of type A over Z are free by giving a graded cellular basis of the cyclotomic KLR algebra. We then extend it to obtain a graded cellular basis of the affine KLR algebra, which indicates that the affine KLR algebra is an affine graded cellular algebra. Finally we work with the Jucys-Murphy elements of the cyclotomic Hecke algebras of type A and proved a periodic property of these elements.The main purpose of this thesis is to prove that the cyclotomic Khovanov-Lauda-Rouquier algebras of type A over Z are free by giving a graded cellular basis of the cyclotomic KLR algebra. We then extend it to obtain a graded cellular basis of the affine KLR algebra, which indicates that the affine KLR algebra is an affine graded cellular algebra. Finally we work with the Jucys-Murphy elements of the cyclotomic Hecke algebras of type A and proved a periodic property of these elements.
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Date
2012-12-12Licence
The author retains copyright of this thesis.Faculty/School
Faculty of Science, School of Mathematics and StatisticsDepartment, Discipline or Centre
Pure MathematicsAwarding institution
The University of SydneyShare