The peak algebra of the symmetric group revisited
| dc.creator | Schocker, Manfred | |
| dc.date | 2002-09-26 | |
| dc.date.accessioned | 2026-07-07T04:51:18Z | |
| dc.date.available | 2026-07-07T04:51:18Z | |
| dc.description | The linear span P_n of the sums of all permutations in the symmetric group S_n with a given set of peaks is a sub-algebra of the symmetric group algebra, due to Nyman. This peak algebra is a left ideal of the descent algebra D_n; and the direct sum P of all P_n is a Hopf sub-algebra of the direct sum D of all D_n, dual to the Stembridge algebra of peak functions. In our self-contained approach, peak counterparts of several results on the descent algebra are established, including a simple combinatorial characterization of the algebra P_n; an algebraic characterization of P_n based on the action on the Poincar'e-Birkhoff-Witt basis of the free associative algebra; the display of peak variants of the classical Lie idempotents; an Eulerian-type sub-algebra of P_n; a description of the Jacobson radical of P_n and its nil-potency index, of the principal indecomposable and irreducible P_n-modules, and of the Cartan matrix of P_n. Furthermore, it is shown that the primitive Lie algebra of P is free, and that P is its enveloping algebra. | |
| dc.description | 60 pages | |
| dc.identifier | https://arxiv.org/abs/math/0209376 | |
| dc.identifier | http://arxiv.org/abs/math/0209376 | |
| dc.identifier | Adv. in Math. 192 (2005), No. 2, 259-309 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65097 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Combinatorics | |
| dc.subject | 16W30*;20C30;17B01;16N20;05E10 | |
| dc.title | The peak algebra of the symmetric group revisited | |
| dc.type | text |