Drinfel'd doubles and Shapovalov determinants

Details Drinfel'd doubles and Shapovalov determinants Drinfel'd doubles and Shapovalov determinants

2008-10-09

arxiv.org/abs/0810.1621v1

Mathematics

Quantum Algebra

50 pages

Scientific paper

The Shapovalov determinant for a class of pointed Hopf algebras is calculated, including quantized enveloping algebras, Lusztig's small quantum groups, and quantized Lie superalgebras. Our main tools are root systems, Weyl groupoids, and Lusztig type isomorphisms. We elaborate powerful novel techniques for the algebras at roots of unity, and pass to the general case using a density argument. Key words: Hopf algebra, Nichols algebra, quantum group, representation

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