Faithful representations of SL(2) over truncated Witt vectors

Abstract

Let G be the six dimensional linear algebraic k-group SL_2(W_2), where W_2 is the ring of Witt vectors of length two over the algebraically closed field k of characteristic p>2. Then the minimal dimension of a faithful rational k-representation of G is p+3.Comment: New title. New section 9 contains a finite group version of the main result. 11 pages, AMS LaTeX. To appear in the Journal of Algebr