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Clifford algebras as deformations of exterior algebras

As Igor mentions in the comments, this is really a question about deformations of the multiplication map of the exterior algebra in the space of associative multiplications. Since this is a pretty ...
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Deformations of Calabi-Yau manifolds

The answer in general is no. Nakamura has constructed here (pp.90, 96-99, solvmanifolds of type III-(3b)) an example of a compact complex (non-Kähler) manifold $M$ with $TM$ holomorphically ...
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DGLA or $L_{\infty}$-algebra controlling the deformation of Einstein metrics and instantons

The Quillen-Drinfeld-Deligne-etc. philosopy should not be looked at as something too mysterious. Namely, it reduces to the fact that if the set of objects one is interesting in the infinitesimal ...
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Exercise 1.1.(c) in Hartshorne's Deformation Theory

I agree. Thanks for discovering the error. And by the way there is another error on the same page, line -1, there is a -2 that should be a -4. Robin Hartshorne

Clifford algebras as deformations of exterior algebras

In addition to the answer of Bertram Arnold, let me point out that there is a very explicit formula for "fermionic" Weyl-Moyal product. Let us assume that your vector space $V$ (or module) is defined ...
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• 18.9k
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Some elementary questions about deformation quantization

a lot of questions, let me try on some of them :) The bad news is that in most of the interesting situations the higher order terms of the star product, the $B_i$ will not vanish. Heuristically this ...
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Some examples of $\mathbb Q$-Gorenstein smoothing
Question 1. The answer is yes, and the classical example is as follows. Is it possible to find a one-parameter family $\psi \colon \mathcal{X} \to \Delta$ such that $X_0$ is isomorphic to the cone ...
I suspect, Deligne's intuition went along the following lines. Deformation theory describes the tangent cone at a point $x$ of the moduli space $M$ of the problem. The tangent cone is Spec Gr \$\...