Representations Parameterized by a Pair of Characters
Abstrak
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.
Topik & Kata Kunci
Penulis (2)
David E. Radford
Hans-Jürgen Schneider
Akses Cepat
- Tahun Terbit
- 2006
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓