On the structure and classification of Bernstein algebras
G. Militaru

TL;DR
This paper characterizes Bernstein algebras by showing they are isomorphic to a specific semidirect product involving a commutative algebra with nilpotent elements and an idempotent endomorphism, providing a classification and automorphism group description.
Contribution
It introduces a new structural description of Bernstein algebras as semidirect products and classifies their types using linear algebra tools.
Findings
Bernstein algebras are isomorphic to a semidirect product involving a commutative algebra with nilpotent elements.
The set of types of Bernstein algebras is explicitly classified using linear algebra.
The automorphism group of Bernstein algebras is described as a subgroup of a canonical semidirect product.
Abstract
We prove that any Bernstein algebra is isomorphic to a semidirect product associated to a commutative algebra such that , for all and an idempotent endomorphism of satisfying two compatibility conditions. The set of types of -dimensional Bernstein algebras is parametrized by an explicitely constructed (using linear algebra tools) classified object. The automorphisms group of any Bernstein algebra is described as a subgroup of the canonical semidirect product of groups .
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Algebra and Logic
