Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Geometric Approach to Hochschild Cohomology of the Exterior Algebra   We give a new computation of Hochschild (co)homology of the exterior algebra,
together with algebraic structures, by direct comparison with the symmetric
algebra. The Hochschild cohomology is determined to be essentially the algebra
of even-weight polyvector fields. From Kontsevich's formality theorem, the
differential graded Lie algebra of Hochschild cochains is proved to be formal
when the vector space generating the exterior algebra is even dimensional. We
conjecture that formality fails in the odd dimensional case, proving this when
the dimension is one. In all dimensions, formal deformations of the exterior
algebra are classified by formal Poisson structures.

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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th