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Description: |
Enveloping algebras of Lie algebras are typical examples of Hopf algebras. Some of them can be presented as iterated Ore extensions, which are a sort of non-commutative polynomial rings. This raises the natural question as to which Ore extensions over a Hopf algebras R admit a Hopf algebra structure that extends the Hopf algebra structure of R. I will review the known results that were obtained by Panov (2003) and Brown, O'Hagan, Zhang and Zhuang (2015). Furthermore I will report on some attempts that I have done together with my PhD students Ricardo Leite dos Santos generalizing Panov's result to the context of weak Hopf algebras in the sense of Böhm, Nil, Szlachanyi (1999). In the second half of my talk I will address the question of which semisimple Hopf algebras act on Ore extensions. An important result by Etingof and Walton (2014) says that any semisimple Hopf algebra action on a commutative domain is given by a group action. Following the arguments given by Cuadra, Etingof and Walton (2014), I showed jointly with my PhD student Deividi Pansera that the same statement is true for actions of semisimple Hopf algebras on iterated Ore extensions, which involve only derivations. If time permits I will also report on Pansera's constructions of semisimple Hopf algebra actions on the quantum plane that are not given by group actions.
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Date: |
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| Start Time: |
15:00 |
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Speaker: |
Christian Lomp (Univ. Porto)
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Institution: |
Universidade do Porto
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Place: |
Room 5.5, Department of Mathematics, U.C.
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| Research Groups: |
-Algebra and Combinatorics
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See more:
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