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• W2155652310 abstract "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." @default.
• W2155652310 created "2016-06-24" @default.
• W2155652310 creator A5040029357 @default.
• W2155652310 creator A5056470367 @default.
• W2155652310 date "2015-03-18" @default.
• W2155652310 modified "2023-09-24" @default.
• W2155652310 title "Hochschild products and global non-abelian cohomology for algebras. Applications" @default.
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• W2155652310 doi "https://doi.org/10.48550/arxiv.1503.05364" @default.
• W2155652310 hasPublicationYear "2015" @default.
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