Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial identities and noncommutative versal torsors   To any cleft Hopf Galois object, i.e., any algebra H[t] obtained from a Hopf
algebra H by twisting its multiplication with a two-cocycle t, we attach two
"universal algebras" A(H,t) and U(H,t). The algebra A(H,t) is obtained by
twisting the multiplication of H with the most general two-cocycle u formally
cohomologous to t. The cocycle u takes values in the field of rational
functions on H. By construction, A(H,t) is a cleft H-Galois extension of a
"big" commutative algebra B(H,t). Any "form" of H[t] can be obtained from
A(H,t) by a specialization of B(H,t) and vice versa. If the algebra H[t] is
simple, then A(H,t) is an Azumaya algebra with center B(H,t). The algebra
U(H,t) is constructed using a general theory of polynomial identities that we
set up for arbitrary comodule algebras; it is the universal comodule algebra in
which all comodule algebra identities of H[t] are satisfied. We construct an
embedding of U(H,t) into A(H,t); this embedding maps the center Z(H,t) of
U(H,t) into B(H,t) when the algebra H[t] is simple. In this case, under an
additional assumption, A(H,t) is isomorphic to B(H,t) \otimes_{Z(H,t)} U(H,t),
thus turning A(H,t) into a central localization of U(H,t). We work out these
constructions in full detail for the four-dimensional Sweedler algebra.

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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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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: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat