On Nichols algebras of diagonal type

Details On Nichols algebras of diagonal type On Nichols algebras of diagonal type

2011-04-01

arxiv.org/abs/1104.0268v3

Mathematics

Quantum Algebra

52 pages. This work is part of the author's PhD Thesis. The third version has a few changes on the relations generating the id

Scientific paper

We give an explicit and essentially minimal list of defining relations of a Nichols algebra of diagonal type with finite root system. This list contains the well-known quantum Serre relations but also many new variations. A conjecture by Andruskiewitsch and Schneider states that any finite-dimensional pointed Hopf algebra over an algebraically closed field of characteristic zero is generated as an algebra by its group-like and skew-primitive elements. As an application of our main result, we prove the conjecture when the group of group-like elements is abelian.

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