Open Research Index

The rank-one Dixmier conjecture for elements of mass at most six

Idris Ali Shaik

Palomar Registrypalomar/PALOMAR-2026-10-05-000006Oct 5, 2026math.RAscore 0

Over any characteristic-zero field, two elements P and Q of the first Weyl algebra satisfying QP-PQ=1 generate the algebra when P has at most six nonzero homogeneous components for deg X=1 and deg Y=-1. The degree, order and mass of Q are unrestricted. The proof combines sparse-polynomial rigidity with internally proved Newton and Weyl-algebra structural results.

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