论文标题
内侧和异形代数
Medial and isospectral algebras
论文作者
论文摘要
本文的目的是对两个新类别的非缔约代数，即所谓的同谱和内侧代数进行系统研究。同一代数$ \ mathbb {a} $是一种通用的交换性非求解代数，其同性恋具有相同的peirce频谱。内侧代数是具有身份$（xy）（zw）=（xz）（yw）$的代数。我们表明，这两个类实质上是一致的。我们还证明，任何内侧光谱代数都是对交换性关联商代数$ \ mathbf {k} [z]/（z^n-1）$的一定同位素变形的同构。
The purpose of this paper is to give a systematic study of two new classes of commutative nonassociative algebras, the so-called isospectral and medial algebras. An isospectral algebra $\mathbb{A}$ is a generic commutative nonassociative algebra whose idempotents have the same Peirce spectrum. A medial algebra is algebra with identity $(xy)(zw)=(xz)(yw)$. We show that these two classes are essentially coincide. We also prove that any medial spectral algebra is isomorphic to a certain isotopic deformation of the commutative associative quotient algebra $\mathbf{K}[z]/(z^n-1)$.
