6 papers
Grün's Lemma for Semiassociative Mal'cev Algebras
Alexander Wires
We extend recent work on analogues of Grün's Lemma from skew-braces to all semiassociative Mal'cev algebras which is a broad class of algebras encompassing all expansions of groups…
Correspondence, Wells and Hochschild-Serre sequences for nonabelian extensions of multiplicative Lie algebras
Alexander Wires, Dev Karan Singh, Shiv Datt Kumar
For nonabelian -cohomology of multiplicative Lie algebras, we properly generalize from the group case three classic results. We prove a Correspondence theorem whic…
Extensions realizing affine datum : central extensions
Alexander Wires
The study of extensions realizing affine datum is specialized to central extensions in varieties with a difference term which leads to generalizations of several classical theorems…
Extensions realizing affine datum : the Wells derivation
Alexander Wires
We develop the Wells derivation for extensions realizing affine datum in arbitrary varieties; in particular, we show there is an exact sequence connecting the group of compatible a…
Extensions of Multilinear Module Expansions
Alexander Wires
We consider the deconstruction/reconstruction of extensions in varieties of algebras which are modules expanded by multilinear operators. The parametrization of extensions determin…
Extension realizing affine datum: low-dimensional cohomology
Alexander Wires
For arbitrary varieties of universal algebras, we develop the theory around the first and second-cohomology groups characterizing extensions realizing affine datum. Restricted to v…