The Decomposition of Lie Powers
| dc.creator | Bryant, R. M. | |
| dc.creator | Schocker, M. | |
| dc.date | 2005-05-16 | |
| dc.date.accessioned | 2026-07-07T05:19:55Z | |
| dc.date.available | 2026-07-07T05:19:55Z | |
| dc.description | Let G be a group, F a field of prime characteristic p and V a finite-dimensional FG-module. Let L(V) denote the free Lie algebra on V regarded as an FG-submodule of the free associative algebra (or tensor algebra) T(V). For each positive integer r, let L^r(V) and T^r(V) be the rth homogeneous components of L(V) and T(V), respectively. Here L^r(V) is called the rth Lie power of V. Our main result is that there are submodules B_1, B_2, ... of L(V) such that, for all r, B_r is a direct summand of T^r(V) and, whenever m \geq 0 and k is not divisible by p, $$ L^{p^mk}(V) = L^{p^m}(B_k) \oplus L^{p^{m-1}}(B_{pk}) \oplus ... \oplus L^p(B_{p^{m-1}k}) \oplus L^1(B_{p^mk}). $$ Thus every Lie power is a direct sum of Lie powers of p-power degree. The approach builds on an analysis of T^r(V) as a bimodule for G and the Solomon descent algebra. | |
| dc.description | 32 pages | |
| dc.identifier | https://arxiv.org/abs/math/0505325 | |
| dc.identifier | http://arxiv.org/abs/math/0505325 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75205 | |
| dc.subject | Representation Theory | |
| dc.subject | 17B01 (Primary), 20C07, 20C20 (Secondary) | |
| dc.title | The Decomposition of Lie Powers | |
| dc.type | text |