Representations Parameterized by a Pair of Characters
| dc.creator | Radford, David E. | |
| dc.creator | Schneider, Hans-Jürgen | |
| dc.date | 2006-03-11 | |
| dc.date.accessioned | 2026-07-07T07:06:47Z | |
| dc.date.available | 2026-07-07T07:06:47Z | |
| dc.description | Let $U$ and $A$ be algebras over a field $k$. We study algebra structures $H$ on the underlying tensor product $U{\otimes}A$ of vector spaces which satisfy $(u{\otimes}a)(u'{\otimes}a') = uu'{\otimes}aa'$ if $a = 1$ or $u' = 1$. For a pair of characters $ρ\in \Alg(U, k)$ and $χ\in \Alg(A, k)$ we define a left $H$-module $L(ρ, χ)$. Under reasonable hypotheses the correspondence $(ρ, χ) \mapsto L(ρ, χ)$ determines a bijection between character pairs and the isomorphism classes of objects in a certain category ${}_H\underline{\mathcal M}$ of left $H$-modules. In many cases the finite-dimensional objects of ${}_H\underline{\mathcal M}$ are the finite-dimensional irreducible left $H$-modules. In math.QA/0603269 we apply the results of this paper and show that the finite-dimensional irreducible representations of a wide class of pointed Hopf algebras are parameterized by pairs of characters. | |
| dc.description | amstex, 33 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603270 | |
| dc.identifier | http://arxiv.org/abs/math/0603270 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110154 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 16W30,17B37, 17B10 | |
| dc.title | Representations Parameterized by a Pair of Characters | |
| dc.type | text |