On baric algebras with prescribed automorphisms
type: Item
instance of: scholarly article
title: On baric algebras with prescribed automorphisms
zbMATH Open document ID: 0586.17014
DOI: 10.1016/0024-3795(86)90022-4
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: The automorphism group of the gametic algebra for a \(2m\)-ploid population with \(n+1\) alleles is isomorphic to \(A(n)\) the affine group of \(\mathbb R^n\). This result is obtained as a special case from a study of automorphisms of slightly more general algebras. The author defines a certain class of algebras called \(\alpha\)-algebras. Roughly speaking, an \(\alpha\)-algebra is a baric algebra in which certain specified linear operators are automorphisms. The definition of these operators is too technical to be given here. The author classifies the \(\alpha\)-algebras for \(m\leq 5\). In a later section he has some results also in the case where \(m>5\). Finally, he claims to have results dealing with derivations of \(\alpha\)-algebras which he says will be published elsewhere.
reviewed by: Harry Gonshor
Mathematics Subject Classification ID: 17D92
zbMATH DE Number: 3939555
zbMATH Keywords: polyploid population
zbMATH Keywords: automorphism group
zbMATH Keywords: gametic algebra
zbMATH Keywords: affine group
zbMATH Keywords: \(\alpha\)-algebras
zbMATH Keywords: baric algebra
author: Luiz Antonio Peresi
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90022-4
OpenAlex ID: W2047629240
cites work: Commutative Train Algebras* of Ranks 2 and 3
cites work: Structure of Genetic Algebras
cites work: Non-Commutative Train Algebras of Ranks 2 and 3
cites work: Special Train Algebras Arising in Genetics
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cites work: Contributions to genetic algebras
cites work: Contributions to genetic algebras II
cites work: Genetic Algebras Considered as Elements in a Vector Space
cites work: Q3869125
cites work: On the derivations of gametic algebras for polyploidy with multiple alleles
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description: scientific article; zbMATH DE number 3939555