Dutch Treat

In the February 1976 Word Ways, Harry Mathews listed more than 250 French words which looked like English words but in reality had entirely different meanings. Here is an analogous list of Dutch words in English dress

Completely reducible Lie subalgebras

Let G be a connected and reductive group over the algebraically closed field K. J-P. Serre has introduced the notion of a G-completely reducible subgroup H of G. In this note, we give a notion of G-complete reducibility -- G-cr for short -- for Lie subalgebras of Lie(G), and we show that if the closed subgroup H < G is G-cr, then Lie(H) is G-cr as well.Comment: 7 pages; AMS LaTeX. To appear in *Transformation Groups

Sub-principal homomorphisms in positive characteristic

Let G be a reductive group over an algebraically closed field of characteristic p, and let u in G be a unipotent element of order p. Suppose that p is a good prime for G. We show in this paper that there is a homomorphism phi:SL_2/k --> G whose image contains u. This result was first obtained by D. Testerman (J. Algebra, 1995) using case considerations for each type of simple group (and using, in some cases, computer calculations with explicit representatives for the unipotent orbits). The proof we give is free of case considerations (except in its dependence on the Bala-Carter theorem). Our construction of phi generalizes the construction of a principal homomorphism made by J.-P. Serre in (Invent. Math. 1996); in particular, phi is obtained by reduction modulo P from a homomorphism of group schemes over a valuation ring in a number field. This permits us to show moreover that the weight spaces of a maximal torus of phi(SL_2/k) on Lie(G) are ``the same as in characteristic 0''; the existence of a phi with this property was previously obtained, again using case considerations, by Lawther and Testerman (Memoirs AMS, 1999) and has been applied in some recent work of G. Seitz (Invent. Math. 2000).Comment: 20 pages, AMS LaTeX. This version fixes some minor glitches, and includes a more detailed section 5.3. To appear in Math. Zeitschrif

Centerscope

Centerscope, formerly Scope, was published by the Boston University Medical Center "to communicate the concern of the Medical Center for the development and maintenance of improved health care in contemporary society.

A survey of business concerns' attitude concerning sponsorship of educational television programs

Thesis (Ed.M.)--Boston Universit

Faithful representations of SL(2) over truncated Witt vectors

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