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for questions about deformation theory, including deformations of manifolds, schemes, Galois representations, and von Neumann algebras.

7 votes
2 answers
379 views

Non-associative deformation quantization

Several physicists consider non-Poisson bivectors but still apply Kontsevich formality in order to get deformation quantization type results: see e.g. Szabos's review An introduction to nonassociative …
Jim Stasheff's user avatar
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4 votes
0 answers
220 views

What does "control of a deformation problem" mean?

Is the expression "control of a deformation problem' ever defined? There are of course many examples relating a dg-Lie or L-infty algebra to a deformation problem, and the phrase is evocative. Is it e …
Jim Stasheff's user avatar
  • 3,880
6 votes
0 answers
315 views

What is the technical difference between a deformation and a perturbation?

What is the technical difference between a deformation and a perturbation? Do they exist in somewhat different categories?
Jim Stasheff's user avatar
  • 3,880
6 votes
3 answers
262 views

graded generalization of the Moyal–Weyl product

Has anyone written about the graded generalization of the Moyal–Weyl product/star product, that is, where the original algebra is already graded? Is it just a matter of signs?
Jim Stasheff's user avatar
  • 3,880
7 votes
2 answers
688 views

Alternative to Kontsevich formality

Has anyone considered an alternative approach to Kontsevich formality in which the DGLA of poly-vector fields is deformed to an $L_\infty$-algebra? Some vocabulary: DGLA = Differential Graded Lie Alg …
Jim Stasheff's user avatar
  • 3,880
3 votes
1 answer
191 views

Koszul algebras deformations

Do we know the maximal class of Koszul algebras for which any deformation is Koszul?
Jim Stasheff's user avatar
  • 3,880
7 votes
0 answers
182 views

Deformation of Noether's first theorem

Noether's first variational theorem establishes a correspondence between symmetries and invariants. I would like to know what has been written on the following question: How do the invariants deform w …
Jim Stasheff's user avatar
  • 3,880