论文标题
张量层次结构代数和限制关联性
Tensor hierarchy algebras and restricted associativity
论文作者
论文摘要
我们研究本地代数，它们的结构类似于$ \ mathbb {z} $ - 分级代数集中在$ -1,0,1 $中，但没有以相同程度$ \ pm1 $的成对元素定义的产品。 To any triple consisting of a Kac-Moody algebra $\mathfrak{g}$ with an invertible and symmetrisable Cartan matrix, a dominant integral weight of $\mathfrak{g}$ and an invariant symmetric bilinear form on $\mathfrak{g}$, we associate a local algebra satisfying a restricted version of associativity.从中，我们通过换向器结构得出了当地的谎言超级船。在某些条件下，我们确定我们显示的生成器满足了以前从相同数据定义的张量层次结构代数$ w $的关系。结果表明，满足这种限制关联的基本结构可能在张量层次结构代数对扩展几何形状的应用中有用。
We study local algebras, which are structures similar to $\mathbb{Z}$-graded algebras concentrated in degrees $-1,0,1$, but without a product defined for pairs of elements at the same degree $\pm1$. To any triple consisting of a Kac-Moody algebra $\mathfrak{g}$ with an invertible and symmetrisable Cartan matrix, a dominant integral weight of $\mathfrak{g}$ and an invariant symmetric bilinear form on $\mathfrak{g}$, we associate a local algebra satisfying a restricted version of associativity. From it, we derive a local Lie superalgebra by a commutator construction. Under certain conditions, we identify generators which we show satisfy the relations of the tensor hierarchy algebra $W$ previously defined from the same data. The result suggests that an underlying structure satisfying such a restricted associativity may be useful in applications of tensor hierarchy algebras to extended geometry.
