Let G be a group. Any G-module M has an algebraic structure called a G-family of Alexander quandles. Given a 2-cocycle of a cohomology associated with this G-family, topological invariants of (handlebody) knots in the 3-sphere are defined. We develop a simple algorithm to algebraically construct n-cocycles of this G-family from G-invariant group n-cocycles of the abelian group M. We present many examples of 2-cocycles of these G-families using facts from (modular) invariant theory.
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