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T. Guédénon 《Algebras and Representation Theory》2008,11(1):25-42
Let k be a field, H a Hopf k-algebra with bijective antipode, A a right H-comodule algebra and C a Hopf algebra with bijective antipode which is also a right H-module coalgebra. Under some appropriate assumptions, and assuming that the set of grouplike elements G(A ⊗ C) of the coring A ⊗ C is a group, we show how to calculate, via an exact sequence, the Picard group of the subring of coinvariants in terms of
the Picard group of A and various subgroups of G(A ⊗ C).
Presented by: Claus Ringel. 相似文献
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Emmanuel Briand Mercedes Rosas Mike Zabrocki 《Journal of Combinatorial Theory, Series A》2008,115(6):1077-1085
Using a noncommutative analog of Chevalley's decomposition of polynomials into symmetric polynomials times coinvariants due to Bergeron, Reutenauer, Rosas, and Zabrocki we compute the graded Frobenius characteristic for their two sets of noncommutative harmonics with respect to the left action of the symmetric group (acting on variables). We use these results to derive the Frobenius series for the enveloping algebra of the derived free Lie algebra in n variables. 相似文献
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Let H be a Hopf algebra over a field k, and A an H-comodule algebra. The categories of comodules and relative Hopf modules are then Grothendieck categories with enough injectives. We study the derived functors of the associated Hom functors, and of the coinvariants functor, and discuss spectral sequences that connect them. We also discuss when the coinvariants functor preserves injectives. 相似文献
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