Multiplicative basis for algebras whose universal cover has no oriented cycles

A Characterization of Surfaces Whose Universal Cover Is the Bidisk

We show that the universal cover of a compact complex surface X is the bidisk H × H, or X is biholomorphic to P × P, if and only if K X > 0 and there exists an invertible sheaf η such that η 2 ∼= OX and H0(X,S2Ω1X(−KX) ⊗ η) 6= 0. The two cases are distinguished by the second plurigenus, P2(X) ≥ 2 in the former case, P2(X) = 0 in the latter. We also discuss related questions.

On Varieties Whose Universal Cover Is a Product of Curves

We investigate a necessary condition for a compact complex manifold X of dimension n in order that its universal cover be the Cartesian product C of a curve C = Por H: the existence of a semispecial tensor ω. A semispecial tensor is a non zero section 0 6= ω ∈ H0(X,SnΩ1X(−KX)⊗ η)), where η is an invertible sheaf of 2-torsion (i.e., η ∼= OX). We show that this condition works out nicely, as a su...

On a Filtered Multiplicative Basis of Group Algebras

Abstract. Let K be a field of characteristic p and G a nonabelian metacyclic finite p-group. We give an explicit list of all metacyclic p-groups G, such that the group algebra KG over a field of characteristic p has a filtered multiplicative K-basis. We also present an example of a non-metacyclic 2-group G, such that the group algebra KG over any field of characteristic 2 has a filtered multipl...

Further results on a filtered multiplicative basis of group algebras ∗

Let FG be a group algebra of a finite non-abelian pgroup G and F a field of characteristic p. In this paper we give all minimal non-abelian p-groups and minimal non-metacyclic p-groups whose group algebras FG possess a filtered multiplicative F -basis.

Cover for Volume.13, No.2