2023/10/01 by Alexander Wires, Wires, Alexander
Mathematics · Medicine · #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2310.00565
openalex publication_date 2023/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the deconstruction/reconstruction of extensions in varieties of algebras which are modules expanded by multilinear operators. The parametrization of extensions determined by abelian ideals with unary actions agrees with the previous development of extensions realizing affine datum in arbitrary varieties of universal algebras. We establish a Well's type theorem which, for a fixed affine ideal, characterizes those ideal-preserving derivations of a group-trivial extension as a Lie algebra extension of the compatible pairs of derivations of the datum algebras associated to the ideal by the cohomological derivations of the datum. For these varieties, we establish a low-dimensional Hochschild-Serre exact sequence associated to an arbitrary extension equipped with an additional affine action.