Abstract

This paper is devoted to the study of four-dimensional commutative power-associative non-Jordan train algebras. The existence of a unique orthogonal idempotent element in such kind of algebras enables us to define a non-zero algebra homomorphism over their ground field, which gives rise to train algebras of rank 4. We describe the irreducible representations over an algebraically closed field of characteristic prime to 30 by means of multilinear identities which define it. Furthermore, we provide sufficient conditions to guarantee whenever a representation is decomposable.

中文翻译：

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等级 4 的幂关联列车代数的表示

摘要

本文致力于研究四维可交换幂结合非Jordan 列代数。在此类代数中存在唯一的正交幂等元素使我们能够在其基域上定义非零代数同态，从而产生 4 阶代数训练。 我们描述了在特征的代数闭域上的不可约表示通过定义它的多线性恒等式将素数设为 30。此外，我们提供了充分的条件来保证表示何时是可分解的。