 
Summary: Z .Journal of Algebra 220, 401 414 1999
Article ID jabr.1999.7860, available online at http:rrwww.idealibrary.com on
Projective Schur Algebras of Nilpotent Type Are
Brauer Equivalent to Radical Algebras*
Eli Aljadeff and Jack Sonn
Department of Mathematics, Technion Israel Institute of Technology,
32000 Haifa, Israel
Communicated by Alexander Lubotzky
Received June 1, 1998
1. INTRODUCTION
2Z .Let k be a field and G a finite group. For any element g H G, k*
Z .k* denotes the units of k, here as a trivial Gmodule , we can form the
twisted group algebra k G. It is isomorphic to the group algebra as a
vector space and its multiplication satisfies the rule
xu yu s xyf , u ,Z .r r
where f: G = G ª k* is a 2cocycle representing . It is easily checked
that the 2cocycle condition satisfied by f ensures the associativity of the
multiplication in k G.
A projective Schur algebra over k is by definition a kcentral simple
algebra which is a homomorphic image of a twisted group algebra k G for
