The Liu-Morin Extension Conjecture
Prior state unknown→proved
Han's conjecture itself remains open; this settles the Liu-Morin extension case
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algebra / Homological algebra
The Liu-Morin Extension Conjecture
Han's conjecture predicts that a finite-dimensional algebra with eventually vanishing Hochschild homology has finite global dimension. Within the tau-Hochschild framework it splits into persistence and survival, and the Liu-Morin extension conjecture concerns when the property passes to extensions. A protected corner theorem bounding Ext at a surviving vertex settles it beyond the monomial and special biserial cases, and yields a trichotomy for failures on three strongly connected vertices.
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Han's conjecture predicts that a finite-dimensional algebra with eventually vanishing Hochschild homology has finite global dimension. Within the tau-Hochschild framework it splits into persistence and survival, and the Liu-Morin extension conjecture concerns when the property passes to extensions. A protected corner theorem bounding Ext at a surviving vertex settles it beyond the monomial and special biserial cases, and yields a trichotomy for failures on three strongly connected vertices.
Han's conjecture itself remains open; this settles the Liu-Morin extension case
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