Let E denote the natural module for the general linear group GL k n over an infinite field k of non-zero characteristic p. We consider here modules which are direct summands of the dth tensor power E md . The original motivation was to study the free Lie algebra. Let L be the d homogeneous component
Module structure of the free Lie ring on three generators
✍ Scribed by L. G. Kovács; Ralph Stöhr
- Publisher
- Springer
- Year
- 1999
- Tongue
- English
- Weight
- 65 KB
- Volume
- 73
- Category
- Article
- ISSN
- 0003-889X
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We prove that, for every regular ring R, there exists an isomorphism between the monoids of isomorphism classes of finitely generated projective right modules Ž Ž . . Ž . over the rings End R and RCFM R , where the latter denotes the ring of R R countably infinite row-and column-finite matrices over
For any representation of a p-group G on a vector space of dimension 3 over a finite field k of characteristic p, we show how the symmetric algebra, regarded as a kG-module, can be expressed as a direct sum of kG-modules, each one of which is isomorphic to a summand in low degree. It follows that, f