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On Nichols algebras of diagonal type
-
Iván Angiono
Veröffentlicht/Copyright:
13. März 2013
Abstract.
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.
Received: 2011-08-01
Revised: 2011-11-19
Published Online: 2013-03-13
Published in Print: 2013-10-01
© 2013 by Walter de Gruyter Berlin Boston
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- Unified approach to the classification of actions of discrete amenable groups on injective factors
- Isoperimetric control of the spectrum of a compact hypersurface
- Weighted divisor sums and Bessel function series. III
- Quasilinear parabolic equations and the Ricci flow on manifolds with boundary
- On the noncommutative Bondal–Orlov conjecture
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Artikel in diesem Heft
- Masthead
- Unified approach to the classification of actions of discrete amenable groups on injective factors
- Isoperimetric control of the spectrum of a compact hypersurface
- Weighted divisor sums and Bessel function series. III
- Quasilinear parabolic equations and the Ricci flow on manifolds with boundary
- On the noncommutative Bondal–Orlov conjecture
- Cohomogeneity one actions on symmetric spaces of noncompact type
- Isoparametric functions and exotic spheres
- The rationality of the moduli spaces of trigonal curves of odd genus
- On Nichols algebras of diagonal type
