Units in finite loop algebras of RA2 loops

Abstract

Let F[L] be the loop algebra of a loop L over a field F. In this paper, we characterize the structure of the unit loop of F[L] modulo its Jacobson radical when L = M(D2m, 2) is an RA2 loop obtained from the dihedral group of order 2m, m is an odd number and F is a finite field of characteristic 2. The structure of 1 + J(F[L]) is also determined.