论文标题
杀死与Steiner Triple Systems有关
Killing metrized commutative nonassociative algebras associated with Steiner triple systems
论文作者
论文摘要
对于每个施泰纳三重系统，都有一个由构造精确的一个参数为可交换，非缔合性，非缔合代数的家族，这意味着每个乘法操作员的痕迹都消失了，并且这些代数被证明被证明正在杀死地层，这意味着杀人类型的痕量形式是非态形和不明式的（frobeniant and Invariant（frobyiant），而不是一定的参数，并且是某些参数，并且是某些参数，并且是某些参数。这些代数的定义类似于Steiner三重系统的Matsuo代数的定义，但它们是不同的。对于霍尔三重系统，相关的代数是$ \ mathbb {z}/2 \ mathbb {z} $的原始轴向代数。
With each Steiner triple system there is associated a one-parameter family of commutative, nonassociative, nonunital algebras that are by construction exact, meaning that the trace of every multiplication operator vanishes, and these algebras are shown to be Killing metrized, meaning the Killing type trace-form is nondegenerate and invariant (Frobenius), and simple, except for certain parameter values. The definition of these algebras resembles that of the Matsuo algebra of the Steiner triple system, but they are different. For a Hall triple system, the associated algebra is a primitive axial algebra for a $\mathbb{Z}/2\mathbb{Z}$-graded fusion law.
