A negative answer to Question 31 (section 2.2.5, page 24, arXiv:2610.22248v1): special linear obstructions for evolution algebras
Year: 2026
Type: preprint
Abstract: 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: Ma, Haobo, Zhang, Wenlin
Institution: National University of Singapore
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225255926