Subalgebras in K[x] of small codimension

Formal Properties in Small Codimension

In this note we extend connectedness results to formal properties of inverse images under proper maps of Schubert varieties and of the diagonal in products of projective rational homogeneous spaces.

On the Codimension of Subalgebras of the Algebra of Matrices over a Field

Small Semisimple Subalgebras of Semisimple Lie Algebras

The goal of Section 2 is to provide a proof of Theorem 2.0.1. Section 3 introduces the necessary facts about Lie algebras and representation theory, with the goal being the proof of Proposition 3.5.7 (ultimately as an application of Theorem 2.0.1), and Proposition 3.3.1. In Section 4 we prove the main theorem, using Propositions 3.3.1 and 3.5.7. In Section 5, we apply the theorem to the special...

On the Cartan Subalgebras of Lie Algebras over Small Fields

In this note we study Cartan subalgebras of Lie algebras defined over finite fields. We prove that a possible Lie algebra of minimal dimension without Cartan subalgebras is semisimple. Subsequently, we study Cartan subalgebras of gl(n, F ). AMS classification: 17B50

Small Subalgebras of Steenrod and Morava Stabilizer Algebras

Let P (j) (resp. S(n)(j)) be the subalgebra of the Steenrod algebra Ap (resp. nth Morava stabilizer algebra) generated by reduced powers Ppi , 0 ≤ i ≤ j (resp. ti, 1 ≤ i ≤ j). In this paper we identify the dual P (j − 1)∗ of P (j − 1) (resp. S(n)(j), for j ≤ n) with some Frobenius kernel (resp. Fpn -points) of a unipotent subgroup G(j + 1) of the general linear algebraic group GLj+1. Using thes...