A negative answer to Question 31 (section 2.2.5, page 24, arXiv:2610.22248v1): special linear obstructions for evolution algebras
Question 31 (section 2.2.5, page 24, arXiv:2610.22248v1) of Kaygorodov–Martín González–Viruel has a negative answer in its algebraic-group and group-scheme formulations: no finite-dimensional complex evolution algebra has full automorphism group SL_n for n=3 or n>=5. We prove Conjecture 5 and answer the semisimple clause of Question 36: the possible semisimple derivation algebras are exactly finite sums of so_m, m>=3. For zero-annihilator algebras, the same restriction holds for the semisimple quotient of the derivation algebra, settling the simple-ideal issue in the comment following Conjecture 5. We distinguish simple ideals from special-linear subalgebras. The abstract-group clause of Question 31 remains outside these conclusions.
Authors
- Wenlin Zhang (ORCID: https://orcid.org/0009-0005-2414-7968)
- Haobo Ma (ORCID: https://orcid.org/0009-0008-4944-977X)
Institutions
- National University of Singapore (SG)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-11-04
- DOI
- https://doi.org/10.5281/zenodo.23957572
- Primary Topic
- Advanced Topics in Algebra
- Type
- preprint