Decomposition of pointwise finite-dimensional ๐1 persistence modules
Decomposition of pointwise finite-dimensional ๐1 persistence modules
We prove that, over an arbitrary field, pointwise finite-dimensional persistence modules indexed by [Formula: see text] decompose uniquely, up to isomorphism, into the direct sum of a bar code and finitely-many Jordan cells. In the language of representation theory, this is a direct sum of string modules and band modules. โฆ