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Frobenius and Cartier algebras of Stanley-Reisner rings
Álvarez Montaner, Josep; Boix, Alberto F.; Zarzuela Armengou, Santiago
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
We study the generation of the Frobenius algebra of the injective hull of a complete Stanley–Reisner ring over a field with positive characteristic. In particular, by extending the ideas used by M. Katzman to give a counterexample to a question raised by G. Lyubeznik and K.E. Smith about the finite generation of Frobenius algebras, we prove that the Frobenius algebra of the injective hull of a complete Stanley–Reisner ring can be only principally generated or infinitely generated. Also, by using our explicit description of the generators of such algebra and applying the recent work by M. Blickle about Cartier algebras and generalized test ideals, we are able to show that the set of F -jumping numbers of generalized test ideals associated to complete Stanley–Reisner rings form a discrete subset inside the non-negative real numbers.
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Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
Frobenius algebras
Stanley-Reisner rings
Frobenius algebras
Cartier algebras
Frobenius, Àlgebra de
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