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- W3026099372 abstract "In this paper, we consider the problem of determining when two tensor networks are equivalent under a heterogeneous change of basis. In particular, to a tensor (or string) diagram in a certain monoidal category (which we call tensor diagrams), we formulate an associated abelian category of representations. Each representation corresponds to a tensor network on that diagram. We then classify which tensor diagrams give rise to categories that are finite, tame, or wild in the traditional sense of representation theory. For those tensor diagrams of finite and tame type, we classify the indecomposable representations. Our main result is that a tensor diagram is wild if and only if it contains a vertex of degree at least three. Otherwise, it is of tame or finite type." @default.
- W3026099372 created "2020-05-29" @default.
- W3026099372 creator A5070939576 @default.
- W3026099372 date "2020-08-01" @default.
- W3026099372 modified "2023-10-09" @default.
- W3026099372 title "A finite-tame-wild trichotomy theorem for tensor diagrams" @default.
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- W3026099372 doi "https://doi.org/10.1016/j.aim.2020.107213" @default.
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