A Symmetric Counterexample to the Snashall--Solberg Conjecture
Abstract
It is shown that the trivial extension of the Xu--Snashall algebra is a symmetric counterexample to the Snashall--Solberg conjecture, which states that the Hochschild cohomology ring of a finite-dimensional algebra modulo nilpotence is a finitely generated algebra. To the best of our knowledge, this is the first known selfinjective counterexample.
Disclosure
“tly the Gerstenhaber algebra structure on the Hochschild cohomology ring of the trivial extension of the Xu–Snashall algebra; however, this task seems to be rather difficult. We have tried to achieve this with the help of the AI assistants ChatGPT and Kimi, but without success. 2. Proof of Theorem B Definition 2.1 ([9]). Let Λ be a 𝐾-algebra. The Hochschild cochain complex of Λ is ∞”
PDF page 2
- Classification
- Brainstorming or outlining
- Multiplier
- 2
- Verified
Structural counts
Pages 5 pdf
Theorems 3 source
Lemmas 0 source
Propositions 2 source
Corollaries 0 source
Definitions 2 source
Displayed equations 16 source
Bibliography entries 18 source
Appendix pages 0 estimated
Count notes
- Source counts use the expanded primary TeX file Counterexample.tex.
- Appendix pages include the first PDF page with an explicit Appendix heading through the final page.