What question did this study set out to answer?

The study aims to demonstrate the structural properties of certain Malcev algebras and superalgebras.

February 28, 2026International Journal of Algebra and Computation0 citations

Kronecker factorization theorems for the exceptional Malcev algebra

Key Points

The study aims to demonstrate the structural properties of certain Malcev algebras and superalgebras.
Proved isomorphism between specific Malcev algebras and direct sums of commutative algebras.
Examined conditions under which Malcev superalgebras can be represented as direct sums.
Confirmed isomorphism between a defined Malcev algebra and a direct sum structure.
Established that a Malcev superalgebra in a specific variety exhibits similar isomorphic properties.

Abstract

We prove that a Malcev algebra Formula: see text that belongs to a certain variety of Malcev algebras Formula: see text such that Formula: see text contains the Formula: see text-dimensional exceptional Malcev algebra Formula: see text is isomorphic to a direct sum Formula: see text, where Formula: see text is a commutative associative algebra. Also, we prove that a Malcev superalgebra Formula: see text in Formula: see text whose even part Formula: see text contains Formula: see text is isomorphic to a direct sum Formula: see text, where Formula: see text is a supercommutative associative superalgebra.

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