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PreprintCC BY 4.0arXiv

Isomorphisms of graded semiconnected algebras

  • Darius Dramburg
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Abstract

Let A• and B• be nonnegatively graded algebras, finitely generated in degrees less than $2$ and with semisimple base rings A0 and B0. We prove that if A ≃ B as ungraded algebras, then A• ≃ B• as graded algebras. This generalises a theorem of Bell and Zhang arXiv:1509.08812 in the connected case A0 = k = B0, and the path-algebra version when A0 and B0 are k-elementary due to Gaddis arXiv:1712.01650. We also discuss some related open problems for graded algebras.

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Cite

BibTeXRIS
BibTeX
@misc{dramburg2026isomorphisms,
  title = {{Isomorphisms of graded semiconnected algebras}},
  author = {Darius Dramburg},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03288},
  eprint = {2609.03288},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03288},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Isomorphisms of graded semiconnected algebras
AU  - Darius Dramburg
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03288
UR  - https://arxiv.org/abs/2609.03288
AB  - Let A_• and B_• be nonnegatively graded algebras, finitely generated in degrees less than $2$ and with semisimple base rings A_0 and B_0. We prove that if A ≃ B as ungraded algebras, then A_• ≃ B_• as graded algebras. This generalises a theorem of Bell and Zhang arXiv:1509.08812 in the connected case A_0 = k = B_0, and the path-algebra version when A_0 and B_0 are k-elementary due to Gaddis arXiv:1712.01650. We also discuss some related open problems for graded algebras.
ER  -