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On Divided-difference semigroups


FitzGerald, DG, On Divided-difference semigroups, International Journal of Algebra and Computation, 21, (1-2) pp. 179-191. ISSN 0218-1967 (2011) [Refereed Article]

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Copyright © 2011 World Scientific Publishing Co.

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DOI: doi:10.1142/S0218196711006121


The Newtonian divided-difference operators generate the nil-Coxeter algebra and semigroup. A bijective correspondence between the nil-Coxeter semigroup and the symmetric group is used to provide braid-like diagrams for the former, and corresponding Reidemeister-type moves for the relations. Conditions are given for similar relations to hold in a skew group ring. Interesting extensions of the nil-Coxeter semigroup are described and given diagrammatic representations.

Item Details

Item Type:Refereed Article
Keywords:Divided-differences; nil-Coxeter algebra; Bruhat order; diagram semigroups;
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Group theory and generalisations
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:FitzGerald, DG (Dr Des FitzGerald)
ID Code:68975
Year Published:2011
Deposited By:Mathematics and Physics
Deposited On:2011-04-11
Last Modified:2012-05-21
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