An upper bound for the lower central series quotients of a free associative algebra
| dc.creator | Dobrovolska, G. | |
| dc.creator | Etingof, P. | |
| dc.date | 2008-01-14 | |
| dc.date | 2008-03-27 | |
| dc.date.accessioned | 2026-07-07T09:28:35Z | |
| dc.date.available | 2026-07-07T09:28:35Z | |
| dc.description | Feigin and Shoikhet conjectured in math/0610410 that successive quotients $B_m(A_n)$ of the lower central series filtration of a free associative algebra $A_n$ have polynomial growth. In this paper we give a proof of this conjecture, using the structure of $W_n$-representation on $B_m(A_n)$ which was defined in math/0610410 . We also prove that the number of squares in a Young diagram $D$ corresponding to an irreducible $W_n$-module in the Jordan-Holder series of $B_m(A_n)$ is bounded above by the integer $(m-1)^2+2[(n-2)/2](m-1)$. This bound combined with MAGMA computations by Rains in math/0610410 allows us to confirm the $W_n$-module structure of $B_3(A_3)$ conjectured in math/0610410 . | |
| dc.description | 7 pages; introduction expanded | |
| dc.identifier | https://arxiv.org/abs/0801.1997 | |
| dc.identifier | http://arxiv.org/abs/0801.1997 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157479 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Representation Theory | |
| dc.title | An upper bound for the lower central series quotients of a free associative algebra | |
| dc.type | text |