Varieties for Modules of Quantum Elementary Abelian Groups
| dc.creator | Pevtsova, Julia | |
| dc.creator | Witherspoon, Sarah | |
| dc.date | 2006-03-16 | |
| dc.date.accessioned | 2026-07-07T07:06:59Z | |
| dc.date.available | 2026-07-07T07:06:59Z | |
| dc.description | We define a rank variety for a module of a noncocommutative Hopf algebra $A = Λ\rtimes G$ where $Λ= k[X_1, ..., X_m]/(X_1^{\ell}, ..., X_m^{\ell})$, $G = ({\mathbb Z}/\ell{\mathbb Z})^m$, and $\text{char} k$ does not divide $\ell$, in terms of certain subalgebras of $A$ playing the role of "cyclic shifted subgroups". We show that the rank variety of a finitely generated module $M$ is homeomorphic to the support variety of $M$ defined in terms of the action of the cohomology algebra of $A$. As an application we derive a theory of rank varieties for the algebra $Λ$. When $\ell=2$, rank varieties for $Λ$-modules were constructed by Erdmann and Holloway using the representation theory of the Clifford algebra. We show that the rank varieties we obtain for $Λ$-modules coincide with those of Erdmann and Holloway. | |
| dc.description | 30 pages, submitted | |
| dc.identifier | https://arxiv.org/abs/math/0603409 | |
| dc.identifier | http://arxiv.org/abs/math/0603409 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110231 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | 16E40; 16W30 | |
| dc.title | Varieties for Modules of Quantum Elementary Abelian Groups | |
| dc.type | text |