Quantum complete intersections, and nonprincipal blocks of finite groups

D. J. Benson
Department of Mathematics, University of Georgia,
Athens GA 30602, USA

E. L. Green
Department of Mathematics, Virginia Polytechnic Institute
and State University, Blacksburg VA 24061, USA

Abstract.

We give a general construction which shows that a 
large class of quantum complete intersections can be realized as
the basic algebras of nonprincipal blocks of finite groups. We
investigate the Ext rings of these algebras. We describe how to
construct a finite $p'$-covering for one of these quantum complete
intersections, which supports a Hopf algebra structure which
is neither commutative nor cocommutative in general. We use this
to investigate a problem concerning the definition of nucleus for
a nonprincipal block.