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Regular evolution algebras are universally finite
- Source :
- Proceedings of the American Mathematical Society. 150:919-925
- Publication Year :
- 2021
- Publisher :
- American Mathematical Society (AMS), 2021.
-
Abstract
- In this paper we show that evolution algebras over any given field $\Bbbk$ are universally finite. In other words, given any finite group $G$, there exist infinitely many regular evolution algebras $X$ such that $Aut(X)\cong G$. The proof is built upon the construction of a covariant faithful functor from the category of finite simple (non oriented) graphs to the category of (finite dimensional) regular evolution algebras. Finally, we show that any constant finite algebraic affine group scheme $\mathbf{G}$ over $\Bbbk$ is isomorphic to the algebraic affine group scheme of automorphisms of a regular evolution algebra.<br />Comment: Minor corrections. Bibliography updated. To appear in Proc. Amer. Math. Soc
- Subjects :
- Pure mathematics
Finite group
Functor
Applied Mathematics
General Mathematics
Field (mathematics)
Mathematics - Rings and Algebras
Automorphism
05C25, 17A36, 17D99
Rings and Algebras (math.RA)
Simple (abstract algebra)
Scheme (mathematics)
Affine group
FOS: Mathematics
Algebraic number
Mathematics
Subjects
Details
- ISSN :
- 10886826 and 00029939
- Volume :
- 150
- Database :
- OpenAIRE
- Journal :
- Proceedings of the American Mathematical Society
- Accession number :
- edsair.doi.dedup.....7a4a7ac3e973233c6e815876cd9ea73a