New York Journal of Mathematics
Volume 10 (2004) 295-306


Alan Koch

Height one Hopf algebras in low ramification

Published: December 31, 2004
Keywords: Hopf algebras, Honda systems
Subject: 16W, 57T, 14L

Let k be a perfect field of characteristic p>0. We obtain a complete classification of finite abelian local k-Hopf algebras with local dual such that the augmentation ideal is annihilated by the Frobenius map. We then use the theory of finite Honda systems to show that these Hopf algebras lift to extensions R of W(k) with 2≦ e(R/W(k))≦ p-1, and construct all such lifts.

Author information

Department of Mathematics, Agnes Scott College, 141 E. College Ave., Decatur, GA 30033