论文标题
具有小衍生理想的联想代数
Associative Algebras with Small Derived Ideal
论文作者
论文摘要
该论文涉及特殊特殊的联想代数，即海森伯格谎言代数的类似物。特别是，我们说联想代数如果其中心等于其派生的理想，并且中心是1维的，则是特别的。在本文中，我们通过证明其结构等效于特殊的特殊莱布尼兹代数的代数来对额外的特殊联想代数进行分类。然后，我们通过维度来表征其（Schur）乘数，并完全确定它们的能力。我们将其与单周代数的相关概念联系起来，并讨论分类额外的特殊DIASSSSSOCIATIVE代数的问题。
The paper concerns extra special associative algebras, an analogue of the Heisenberg Lie algebra. In particular, we say that an associative algebra is extra special if its center is equal to its derived ideal and the center is 1-dimensional. In this paper, we classify extra special associative algebras by proving that their structure is equivalent to that of extra special Leibniz algebras. We then characterize their (Schur) multipliers via dimension and completely determine their capability. We connect this with the related notion of unicentral algebras and discuss the problem of classifying extra special diassociative algebras.
