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.

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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
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preprint

A negative answer to Question 31 (section 2.2.5, page 24, arXiv:2610.22248v1): special linear obstructions for evolution algebras

Wenlin Zhang, Haobo Ma
Zenodo (CERN European Organization for Nuclear Research)
Advanced Topics in Algebra
preprint

A negative answer to Question 31 (section 2.2.5, page 24, arXiv:2610.22248v1): special linear obstructions for evolution algebras

Wenlin Zhang, Haobo Ma
preprint en

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.

Zenodo (CERN European Organization for Nuclear Research)
National University of Singapore (SG)
Advanced Topics in Algebra
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