论文标题
原始轴向代数的结构
Structure of primitive axial algebras
论文作者
论文摘要
“融合规则”是同性恋特征空间之间乘法的定律。该术语相对较新，与原始轴向代数密切相关，该代数最近由Hall，Rehren和Sheptorov引入。反过来，轴向代数与$ 3 $ - 转移组和顶点操作员代数密切相关。 在较早的工作中，我们研究了原始的轴向代数，不一定是合理的，并表明它们都有约旦的类型。在本文中，我们表明，所有有限生成的原始轴向代数都是特定描述的柔性有限尺寸非共同代数的直接总和，以及由同一类型的原始轴产生的交换轴向代数。特别是，所有原始的轴向代数都是灵活的。他们也有Frobenius形式。我们对两个原始轴产生的轴向代数的所有原始轴进行精确描述。
"Fusion rules" are laws of multiplication among eigenspaces of an idempotent. This terminology is relatively new and is closely related to primitive axial algebras, introduced recently by Hall, Rehren, and Shpectorov. Axial algebras, in turn, are closely related to $3$-transposition groups and vertex operator algebras. In earlier work we studied primitive axial algebras, not necessarily commutative, and showed that they all have Jordan type. In this paper, we show that all finitely generated primitive axial algebras are direct sums of specifically described flexible finite dimensional noncommutative algebras, and commutative axial algebras generated by primitive axes of the same type. In particular,all primitive axial algebras are flexible. They also have Frobenius forms. We give a precise description of all the primitive axes of axial algebras generated by two primitive axes.
