Quantum groups and representations with highest weight

Details Quantum groups and representations with highest weight Quantum groups and representations with highest weight

1997-04-08

arxiv.org/abs/q-alg/9704007v1

Mathematics

Quantum Algebra

6 pages, AmsTeX

Scientific paper

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 categories---they 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 $\Sigma$.

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