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On divided-difference semigroups
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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 |
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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 <http://ejournals.worldscientific.com.sg/ijac/ijac.shtml> |
Item Statistics: | View statistics for this item |
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