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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, 21 (1-2). pp. 179-191. ISSN 0218-1967 (Submitted)

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Abstract

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
Keywords: Keywords: divided-di¤erences, nil-Coxeter algebra, Bruhat order, diagram semigroups, presentations.
Journal or Publication Title: International Journal of Algebra and Computation
Page Range: pp. 179-191
ISSN: 0218-1967
Identification Number - DOI: 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 <http://ejournals.worldscientific.com.sg/ijac/ijac.shtml>
Date Deposited: 23 Dec 2009 23:19
Last Modified: 18 Nov 2014 04:08
URI: http://eprints.utas.edu.au/id/eprint/9556
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