Cellular algebras.
Let and be two pointed sets. Given a family of three maps , this family provides an adequate decomposition of as the orthogonal disjoint union of well-described -invariant subsets. This decomposition is applied to the structure theory of graded involutive algebras, graded quadratic algebras and graded weak -algebras.
Let be a division ring finite dimensional over its center . The goal of this paper is to prove that for any positive integer there exists the th multiplicative derived subgroup such that is a maximal subfield of . We also show that a single depth- iterated additive commutator would generate a maximal subfield of
In this paper a construction of characteristic classes for a subfoliation is given by using Kamber-Tondeur’s techniques. For this purpose, the notion of -foliated principal bundle, and the definition of its associated characteristic homomorphism, are introduced. The relation with the characteristic homomorphism of -foliated bundles, , the results of Kamber-Tondeur on the cohomology of --algebras. Finally, Goldman’s results on the restriction of foliated bundles to the leaves of a foliation...
Given a principal ideal domain of characteristic zero, containing 1/2, and a two-cone of appropriate connectedness and dimension, we present a sufficient algebraic condition, in terms of Adams-Hilton models, for the Hopf algebra to be isomorphic with the universal enveloping algebra of some -free graded Lie algebra; as usual, stands for free part, for homology, and for the Moore loop space functor.