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Applying the Reidemeister-Schreier process to the alternating Hecke algebra
by
Leah Ratliff
University of Sydney
We define the alternating Hecke algebra as the subalgebra of the Iwahori-Hecke algebra which is fixed under a certain involution. In the case of the symmetric group, it is a q-analogue of the alternating group.
The Reidemeister-Shreier rewriting process enables us to find a presentation for a subgroup given we already know a presentation for the containing group.
We show how to generalise the Reidemeister-Shreier process in order to obtain a presentation for a subalgebra of an algebra. We then apply this to obtain a presentation for the alternating Hecke algebra.
Date received: September 17, 2003
Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cala-18.