2002/08/20 by M. Domokos, M Domokos, Domokos, M +3
Mathematics · Physics and Astronomy · #16W30 #20G42 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16W30 #msc:20G42
paper · pdf · doi:10.48550/arxiv.math/0208142
20 pages
arxiv created 2002/08/20 · openalex publication_date 2002/08/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A 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 S2-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.