Authors’ abstract: Let \(F\) be a field of characteristic 0 and let \(\lambda_{i,j}\in F^*\) for \(1\leq i,j\leq n\). Define \(R=F[\overline x_1,\overline x_2,\dots,\overline x_n]\) to be the skew polynomial ring with \(\overline x_i\overline x_j=\lambda_{i,j}\overline x_j\overline x_i\) and let \(S=F[\overline x_1,\overline x_2,\dots,\overline x_n,\overline x_1^{-1},\overline x_2^{-1},\dots,\overline x_n^{-1}]\) be the corresponding Laurent polynomial ring. In a recent paper, Kirkman, Procesi, and Small considered these two rings under the assumption that \(S\) is simple and showed, for example, that the Lie ring of inner derivations of \(S\) is simple. Furthermore, when \(n=2\), they determined the automorphisms of \(S\), related its ring of inner derivations to a certain block algebra, and proved that every derivation of \(R\) is the sum of an inner derivation and a derivation which sends each \(x_i\) to a scalar multiple of itself. In this paper, we extend these results to a more general situation. Specifically, we study twisted group algebras \(F^t[G]\) where \(G\) is a commutative group and \(F\) is a field of any characteristic. Furthermore, we consider certain subalgebras \(F^t[H]\) where \(H\) is a subsemigroup of \(G\) which generates \(G\) as a group. Finally, if \(e:G\times G\to F\) is a skew-symmetric bilinear form, then we study the Lie algebra \(F_e[G]\) associated with \(e\), and we consider its relationship to the Lie structure defined on various twisted group algebras \(F^t[G]\).