Frobenius algebras of stanley-reisner rings and maximal free pairs

• Autores: Alberto F. Boix, Santiago Zarzuela
• Localización: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 1132-6360, Nº. 43, 2018 (Ejemplar dedicado a: Proceedings of the XVI EACA Zaragoza Encuentros de Algebra Computacional y Aplicaciones), págs. 87-90
• Idioma: inglés
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• Resumen

  • It is known that the Frobenius algebra of the injective hull of the residue field of a formal power series ring modulo a squarefree monomial ideal can be only principally generated or infinitely generated as algebra over its degree zero piece, and that this fact can be read off in the corresponding simplicial complex; in the infinite case, we exhibit a 1–1 correspondence between potential new generators appearing on each graded piece and certain pairs of faces of such a simplicial complex, that we call maximal free pairs.