Cohomology, Extensions and Automorphisms of Skew Braces
Nishant, Manoj K. Yadav
TL;DR
This paper develops a cohomology theory for left skew braces, linking it to extensions and automorphisms, and introduces a Wells' like exact sequence to relate these concepts.
Contribution
It defines the second cohomology group for left skew braces with trivial coefficients and establishes its connection to extensions and automorphisms, including a new exact sequence.
Findings
Defined the second cohomology group for left skew braces.
Connected cohomology with brace extensions.
Constructed a Wells' like exact sequence.
Abstract
The second cohomology group of a left skew brace with coefficients in a trivial left brace with non-trivial actions is defined, its connection with extensions of a left skew brace by a trivial braces is established and a Wells' like exact sequence relating the second cohomology group with inducible automorphisms of an extension of left skew braces is constructed.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Algebra and Geometry