Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum torsors   This text gives some results about quantum torsors. Our starting point is an
old reformulation of torsors recalled recently by Kontsevich. We propose an
unification of the definitions of torsors in algebraic geometry and in Poisson
geometry. Any quantum torsor is equipped with two comodule-algebra structures
over Hopf algebras and these structures commute with each other. In the finite
dimensional case, these two Hopf algebras share the same finite dimension. We
show that any Galois extension of a field is a torsor and that any torsor is a
Hopf-Galois extension. We give also examples of non-commutative torsors without
character. Torsors can be composed. This leads us to define a new
group-invariant, its torsors invariant. We show how Parmentier's quantization
formalism of "affine Poisson groups" is part of our theory of torsors.

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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph