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On divided-difference semigroups


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FitzGerald, DG 2011 , 'On divided-difference semigroups' , International Journal of Algebra and Computation, vol. 21, no. 1-2 , pp. 179-191 , doi: 10.1142/S0218196711006121.

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The Newtonian divided-di¤erence 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 Type: Article
Authors/Creators:FitzGerald, DG
Keywords: Keywords: divided-di¤erences, nil-Coxeter algebra, Bruhat order, diagram semigroups, presentations.
Journal or Publication Title: International Journal of Algebra and Computation
ISSN: 0218-1967
DOI / ID Number: 10.1142/S0218196711006121
Additional Information:

Author version dated December 21, 2009--Preprint of an article submitted for consideration in International Journal of Algebra and Computation © 2009 World Scientific Publishing Company <>

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