Mathematics – Quantum Algebra
Scientific paper
2006-03-11
Mathematics
Quantum Algebra
amstex, 33 pages
Scientific paper
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 $\rho \in \Alg(U, k)$ and $\chi \in \Alg(A, k)$ we define a left $H$-module $L(\rho, \chi)$. Under reasonable hypotheses the correspondence $(\rho, \chi) \mapsto L(\rho, \chi)$ 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.
Radford David E.
Schneider Hans-Jürgen
No associations
LandOfFree
Representations Parameterized by a Pair of Characters does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Representations Parameterized by a Pair of Characters, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representations Parameterized by a Pair of Characters will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-532850