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PreprintarXiv licencearXiv

Minimal presentations of finite-dimensional representations of pseudocompact algebras

  • Christof Geiss
  • Carolin Hartung
  • Daniel Labardini-Fragoso
  • Jan Schröer
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Abstract

We give a general formula for minimal projective presentations and for minimal discrete-injective presentations of finite-dimensional modules over basic pseudocompact algebras. We also show that the representation-theoretic g-vector of a module coincides with its DWZ-g-vector. These results generalize the description that Derksen, Weyman and Zelevinsky gave of minimal projective presentations for modules over certain finite-dimensional Jacobian algebras. In particular, we can drop their finiteness assumption, and we may work over fields of arbitrary characteristic.

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Cite

BibTeXRIS
BibTeX
@misc{geiss2026minimal,
  title = {{Minimal presentations of finite-dimensional representations of pseudocompact algebras}},
  author = {Christof Geiss and Carolin Hartung and Daniel Labardini-Fragoso and Jan Schröer},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18805},
  eprint = {2610.18805},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18805},
}
RIS
TY  - UNPB
TI  - Minimal presentations of finite-dimensional representations of pseudocompact algebras
AU  - Christof Geiss
AU  - Carolin Hartung
AU  - Daniel Labardini-Fragoso
AU  - Jan Schröer
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18805
UR  - https://arxiv.org/abs/2610.18805
AB  - We give a general formula for minimal projective presentations and for minimal discrete-injective presentations of finite-dimensional modules over basic pseudocompact algebras. We also show that the representation-theoretic g-vector of a module coincides with its DWZ-g-vector. These results generalize the description that Derksen, Weyman and Zelevinsky gave of minimal projective presentations for modules over certain finite-dimensional Jacobian algebras. In particular, we can drop their finiteness assumption, and we may work over fields of arbitrary characteristic.
ER  -