Abstract
By analogy with the Mumford definition of geometrically reductive algebraic group, we introduce the concept of geometrically reductive Hopf algebra (over a field). Then we prove that if H is a geometrically reductive Hopf algebra and A is a commutative, finitely generated and locally finite H-module algebra, then the algebra of invariants A H is finitely generated. We also prove that in characteristic 0 a Hopf algebra H is geometrically reductive if and only if every finite dimensional H-module is semisimple, and that in positive characteristic every finite dimensional Hopf algebra is geometrically reductive. Finally, we prove that in positive characteristic the quantum enveloping Hopf algebras U q ( sl ( n ) ) , n ⩾ 2 , are geometrically reductive for any parameter q ≠ ± 1 .
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
