论文标题
lie代数的结合性张量同构
Tensor Isomorphism by conjugacy of Lie algebras
论文作者
论文摘要
我们引入了一种算法来决定张量之间的同构。该算法使用张量的衍生物的Lie代数来压缩搜索发生在所谓的致密空间的空间。为了使该方法可行，我们给出了一种多项式时算法，以解决通用类模块类别的模块同构的概括。结果，我们表明，同构测试是在多项式时间内的张量，其衍生代数为经典的代数代数，其浓缩空间是1维的。该方法已在岩浆计算机代数系统中实现。
We introduce an algorithm to decide isomorphism between tensors. The algorithm uses the Lie algebra of derivations of a tensor to compress the space in which the search takes place to a so-called densor space. To make the method practicable we give a polynomial-time algorithm to solve a generalization of module isomorphism for a common class of Lie modules. As a consequence, we show that isomorphism testing is in polynomial time for tensors whose derivation algebras are classical Lie algebras and whose densor spaces are 1-dimensional. The method has been implemented in the Magma computer algebra system.
