CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR 


Speaker:       Lindsay Childs, University at Albany 

Time:          Wednesday, February 9, at 4:30pm       

Place:         Earth Sciences 152A, Univ. at Albany 

Title:         Constructing Hopf orders in abelian group rings 


Abstract:

Let  R  be the valuation ring of  K,  a finite extension of the p-adic
rational numbers, and let  G  be a finite abelian p-group. We survey some
results on constructing families of R-Hopf orders in  KG.  There is a
complete classification of Hopf orders in  KG  only for  G  of order  p  
(Tate and Oort) or  p^2  (Greither, Byott and Underwood). For  G  of 
order  p^n  with  n > 2,  several new families have been constructed in 
the past three years, but they do not capture all the possible Hopf orders. 
We will focus on  G  elementary abelian and describe results in a new joint 
paper with Hal Smith, in which constructing examples can be aided by the
simplex algorithm.

 
Refreshments at 4:15pm in ES 152.