Arithmetic Witt-hom-Lie algebras (Q2655927)

Let \(A\) be a \(\Lambda\)-algebra, \(L\) an \(A\)-module, \(\langle-,-\rangle\) an alternating \(\Lambda\)-bilinear form on \(L\). \((L,\langle-,-\rangle,\sigma)\) is called a hom-Lie algebra if the so-called hom-Jacobi identity is satisfied. Now assume that \(G\) acts as a group of \(\Lambda\)-automorphisms on \(L\). A \(G\)-hom-Lie structure on \(L\) is a family of hom-Lie algebras \textbf{L}\((G)=\{(L,\langle-,-\rangle_{\sigma},\sigma)|\sigma\in G\}\). The author proposes a family of hom-Lie structures on group rings with multiplication deformed by a symmetric cocycle. Then he indicates some possible applications in number theory.