Decidability of quasi-isomorphism for semifree DGAs
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Can quasi-isomorphism be decided for semifree noncommutative differential graded algebras over a nontrivial computable unital commutative ring? The target is undecidability under these coefficient and algebra hypotheses.
Why it matters and what counts as progress
Why it matters: It asks whether quasi-isomorphism of the stated algebras can be decided, beyond comparing a list of computable invariants.
What counts as progress: An undecidability reduction for quasi-isomorphism under the specified ring and DGA hypotheses; agreement of computable invariants alone is insufficient.
How the problem developed
- 2026 · Open problem [1]
R. İnanç Baykur, Robion C. Kirby and Daniel Ruberman, editors K3 Problem 5.16 includes deciding quasi-isomorphism for semifree DGAs in its noncommutative and graded-commutative forms.
- 28 Apr 2026 · Reported undecidability theorem [2]
Ciprian Manolescu and Nick Rozenblyum Reported undecidability of quasi-isomorphism for semifree noncommutative DGAs over nontrivial Turing-computable commutative rings.
AI contribution
Undecidability problems for semifree DG algebras
For semifree noncommutative differential graded algebras over a nontrivial computable unital commutative ring, stable tame isomorphism, quasi-isomorphism and derived Morita equivalence are undecidable.
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