Generator and relation ranks for finite-dimensional nilpotent Lie algebras.
The paper contains characterizations of generators and cyclic projective generators in the category of ordered right acts over an ordered monoid.
We continue the study of the category of functors , associated to ₂-vector spaces equipped with a nondegenerate quadratic form, initiated in J. Pure Appl. Algebra 212 (2008) and Algebr. Geom. Topology 7 (2007). We define a filtration of the standard projective objects in ; this refines to give a decomposition into indecomposable factors of the first two standard projective objects in : and . As an application of these two decompositions, we give a complete description of the polynomial functors...
We study the genus and SNT sets of connective covering spaces of familiar finite CW-complexes, both of rationally elliptic type (e.g. quaternionic projective spaces) and of rationally hyperbolic type (e.g. one-point union of a pair of spheres). In connection with the latter situation, we are led to an independently interesting question in group theory: if f is a homomorphism from Gl(ν,A) to Gl(n,A), ν < n, A = ℤ, resp. , does the image of f have infinite, resp. uncountably infinite, index in...