theorem · fr-1-theorem-6-1

Failure of face-compatible completion

Result stated and proved in the source manuscript; website restatement fusion-reconstruction

Statement

For an infinite-index subgroup inclusion, the adjacent algebraic multiplication maps on cannot all extend as bounded or closable operators on the corresponding levelwise Connes-fusion completions . Failure already occurs at depth two.

Meaning and scope

The algebraic multiplication identities still hold. The dual operator-valued weight still realizes the face on its finite ideal. This is an obstruction to the specified ordinary Hilbert-operator realization.

The paper page includes the reader corrections accompanying this edition.

Source

[Paper 1, Theorem 6.1](/public/papers/released/Paper I - Infinite Index Fusion.pdf#page=7). Research note — not peer reviewed.

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