Nil-Coxeter algebra

In mathematics, the nil-Coxeter algebra, introduced by Fomin & Stanley (1994), is an algebra similar to the group algebra of a Coxeter group except that the generators are nilpotent.

Definition

The nil-Coxeter algebra for the infinite symmetric group is the algebra generated by u1, u2, u3, ... with the relations

These are just the relations for the infinite braid group, together with the relations u2
i
 = 0. Similarly one can define a nil-Coxeter algebra for any Coxeter system, by adding the relations u2
i
 = 0 to the relations of the corresponding generalized braid group.

References

This article is issued from Wikipedia - version of the Friday, September 02, 2011. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.