Frobenius and Cartier Algebras of Stanley–Reisner Rings (II)

Alberto F. Boix, Santiago Zarzuela

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

It is known that the Frobenius algebra of the injective hull of the residue field of a complete Stanley–Reisner ring (i.e., 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, and we use it to provide an alternative proof of the fact that these Frobenius algebras can only be either principally generated or infinitely generated.

Original languageEnglish
Pages (from-to)571-586
Number of pages16
JournalActa Mathematica Vietnamica
Volume44
Issue number3
DOIs
StatePublished - 15 Sep 2019

Keywords

  • Cartier algebras
  • Free faces
  • Frobenius algebras
  • Simplicial complexes
  • Stanley–Reisner rings

ASJC Scopus subject areas

  • Mathematics (all)

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