The geometric reductivity of the quantum group \(SL_q(2)\). (English) Zbl 1234.16021
The main result of the paper asserts that in positive characteristic the quantum group \(SL_q(2)\) is geometrically reductive for any \(q\). To prove this the authors extent the concept of geometrically coreductive Hopf algebras to not necessarily commutative Hopf algebras and establish various characterizations of such Hopf algebras. The authors also show that the Hopf algebra \(K[SL_{-1}(2)]\) is geometrically coreductive in any characteristic.
Reviewer: Volodymyr Mazorchuk (Uppsala)
MSC:
16T05 | Hopf algebras and their applications |
16T20 | Ring-theoretic aspects of quantum groups |
17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
16W22 | Actions of groups and semigroups; invariant theory (associative rings and algebras) |
20G42 | Quantum groups (quantized function algebras) and their representations |