Tensor-Ideal-Operator Correspondence

Tensor generalizations of standard linear algebra (for example rank, eigen and singular values) are now known to be NP-hard. But tensors are not only generalized linear algebra. Tensors can just as well be studied as generalized non-associative algebra. I will survey a number of polynomial-time algorithm for tensor structure made possible from this perspective leading to a summary result: Lie algebras, not associative rings, are the universal coefficients for tensor products.