Baer semirings and Baer *-semirings of cone-preserving maps Original Research Article

It is shown that the 2-modular reduction phi of the smallest nontrivial, rational, absolutely irreducible character X of Lyonsʹ sporadic simple group Ly is irreducible. Furthermore, an explicit 45,694-dimensional irreducible matrix representation of Ly over the field GF(2) with two elements is given. The construction has been performed on a parallel computer of type IBM SP1 with 10 nodes. It uses the recent presentation of Ly as a permutation group on 9,606,125 points given by Cooperman, Finkelstein, Tselman, and York.