On the semisimple twisted group algebras of primary cyclic groups (Q2716491)

Let \(p\) be a prime, let \(K\) be a field of characteristic \(\neq p\), and let \(G\) be a cyclic \(p\)-group of order \(p^n\). Then any twisted group algebra \(K_tG\) is isomorphic to \(K[x]/(x^{p^n}-a)\) for some \(0\neq a\in K\). Hence, any decomposition of \(K_tG\) into a direct sum of fields corresponds to a factorization of \(x^{p^n}-a\) into irreducible polynomials. The basic assumption here is that \(K\) is a field of the second kind with respect to \(p\), so that \(\varepsilon_j\in K[\varepsilon_2]\) for all \(j\), where \(\varepsilon_j\) denotes a primitive \(p^j\)-th root of unity. This paper completes earlier work of the authors on this factorization by considering the more difficult \(p=2\) case.