Submission date: 27 July 2024

Abstract:

A “tensor space” is a vector space equipped with a finite collection of multi-linear forms. In previous work, we showed that (for each signature) there exists a universal homogeneous tensor space, which is unique up to isomorphism. Here we generalize that result: we show that each Zariski class of tensor spaces contains a weakly homogeneous space, which is unique up to isomorphism; here, we say that two tensor spaces are “Zariski equivalent” if they satisfy the same polynomial identities. Our work relies on the theory of GL-varieties developed by Bik, Draisma, Eggermont, and Snowden.

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Full text arXiv 2407.19132: pdf, ps.