Quantum groups and representations with highest weight
Abstract
We consider a special category of Hopf algebras, depending on parameters $\Sigma$ which possess properties similar to the category of representations of simple Lie group with highest weight $\lambda$. We connect quantum groups to minimal objects in this categoriesthey correspond to irreducible representations in the category of representations with highest weight $\lambda$. Moreover, we want to correspond quantum groups only to finite dimensional irreducible representations. This gives us a condition for $\lambda$: $\lambda$ is dominant means the minimal object in the category of representations with highest weight $\lambda$ is finite dimensional. We put similar condition for $\Sigma$. We call $\Sigma$ dominant if the minimal object in corresponding category has polynomial growth. Now we propose to define quantum groups starting from dominant parameters $\Sigma$.
 Publication:

eprint arXiv:qalg/9704007
 Pub Date:
 April 1997
 DOI:
 10.48550/arXiv.qalg/9704007
 arXiv:
 arXiv:qalg/9704007
 Bibcode:
 1997q.alg.....4007B
 Keywords:

 Mathematics  Quantum Algebra
 EPrint:
 6 pages, AmsTeX