This paper answers a question posed by Jean-Pierre Serre; namely, a proof is given that if V is a semisimple finite dimensional representation of a group G over Ε½ . m a field K of characteristic p ) 0, and m dim V y mp, then H V is again a K semisimple representation of G.
Acyclicity of Symmetric and Exterior Powers of Complexes
β Scribed by Alexandre B. Tchernev
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 264 KB
- Volume
- 184
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Theorem 1 [Be, Corollary 2.1]. Each permutation in the alternating group A n , n 2, is a product of two l-cycles in S n if and only if either w 3n 4 x l n or n=4 and l=2. Note. Theorem 1 implies that when n=4 every even permutation is a product of two l-cycles if and only if 2 l 4. The aim of the
## Abstract We consider a coupled finite element (fe)βboundary element (be) approach for threeβdimensional magnetic field problems. The formulation is based on a vector potential in a bounded domain (fe) and a scalar potential in an unbounded domain (be). We describe a coupled variational problem y