Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hochschild products and global non-abelian cohomology for algebras.
  Applications   Let $A$ be a unital associative algebra over a field $k$, $E$ a vector space
and $\pi : E \to A$ a surjective linear map with $V = {\rm Ker} (\pi)$. All
algebra structures on $E$ such that $\pi : E \to A$ becomes an algebra map are
described and classified by an explicitly constructed global cohomological type
object ${\mathbb G} {\mathbb H}^{2} \, (A, \, V)$. Any such algebra is
isomorphic to a Hochschild product $A \star V$, an algebra introduced as a
generalization of a classical construction. We prove that ${\mathbb G} {\mathbb
H}^{2} \, (A, \, V)$ is the coproduct of all non-abelian cohomologies ${\mathbb
H}^{2} \, \, (A, \, (V, \cdot))$. The key object ${\mathbb G} {\mathbb H}^{2}
\, (A, \, k)$ responsible for the classification of all co-flag algebras is
computed. All Hochschild products $A \star k$ are also classified and the
automorphism groups ${\rm Aut}_{\rm Alg} (A \star k)$ are fully determined as
subgroups of a semidirect product $A^* \, \ltimes \bigl(k^* \times {\rm
Aut}_{\rm Alg} (A) \bigl)$ of groups. Several examples are given as well as
applications to the theory of supersolvable coalgebras or Poisson algebras. In
particular, for a given Poisson algebra $P$, all Poisson algebras having a
Poisson algebra surjection on $P$ with a $1$-dimensional kernel are described
and classified.

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The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas