Weakly multiplicative coactions of quantized function algebras

Simple item page
dc.creatorDomokos, M
dc.creatorLenagan, T H
dc.date2002-08-20
dc.date.accessioned2026-07-07T04:50:18Z
dc.date.available2026-07-07T04:50:18Z
dc.descriptionA condition is identified which guarantees that the coinvariants of a coaction of a Hopf algebra on an algebra form a subalgebra, even though the coaction may fail to be an algebra homomorphism. A Hilbert Theorem (finite generation of the subalgebra of coinvariants) is obtained for such coactions of a cosemisimple Hopf algebra. This is applied to two adjoint coactions of quantized function algebras of classical groups on the associated FRT bialgebra. Provided that the Hopf algebra is cosemisimple and coquasitriangular, the algebras of coinvariants form two finitely generated, commutative, graded subalgebras which have the same Hilbert series. Consequently, the cocommutative elements and the S^2-cocommutative elements in the Hopf algebra form finitely generated subalgebras. A Hopf algebra monomorphism from the quantum general linear group to Laurent polynomials over the quantum special linear group is found and used to explain the strong relationship between the corepresentation (and coinvariant) theories of these quantum groups.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/math/0208142
dc.identifierhttp://arxiv.org/abs/math/0208142
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64741
dc.subjectQuantum Algebra
dc.subjectRings and Algebras
dc.subject16W30; 20G42
dc.titleWeakly multiplicative coactions of quantized function algebras
dc.typetext

Files

Collections

arXiv