Finite Semisimple Loop Algebras of Indecomposable RA Loops

Abstract

Abstract. There are at the most seven classes of finite indecomposable RA loops upto isomorphism. In this paper, we completely characterize the structure of the unit loop of loop algebras of these seven classes of loops over finite fields of characteristic greater than 2.

Units in finite loop algebras of RA2 loops

“…The semisimple loop algebras of RA loops have been studied by Ferraz, Goodaire and Milies [2]. The structure of the unit loops of finite loop algebras of RA loops of order 32, 64 and in general of seven nonisomorphic classes of indecomposable RA loops have been determined by authors in [8][9][10]. But the problem of characterizing the structure of the unit loops of loop algebras of RA2 loops over finite fields is still open.…”