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A combinatorial criterion for polynomial growth of partially ordered sets which are not simply connected is given. It is obtained by use of Galois covering techniques applied to poset representations. For this purpose a relative version of the basic Galois covering theory of k -categories is...
This paper concerns three classes of geometric 2-complexes of nonpositive curvature: one in which all of the 2-cells are squares, one in which they are all equilateral triangles, and one in which they are all regular hexagons. (These cases correspond to the three regular tessellations of the...
Let (G,K) be a compact Lie pair. Then K acts on the homogeneous space G/K by left translation. In (3), Shiga has studied the condition on the pair (G,K) that the fibration G/K → EK× K G/K → BK is totally non-cohomologous to zero with respect to the real field from the viewpoint of the...
In this paper, we classify torsion theories in the category of graded comodules over a graded coalgebra. Moreover, we give a structure theorem for divisorially graded coalgebras in terms of Picard groups.
In this paper we carry out a systematic study of modules over a formal triangular matrix ring T= A 0 M B . Using the alternative description of right T -modules as triples (X,Y) f with X ∈ Mod−A , Y ∈ Mod−B and f : Y ⊗ B M → X in Mod−A, we shall characterize respectively uniform,...
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