Let T (X) be the tensor bialgebra over an alphabet X. It is a graded connected cocommutative bialgebra, canonically isomorphic to the envelopping bialgebra of the free Lie algebra over X, Lie(X). The subalgebra of its convolution algebra generated by the projections arising from the graduation is also an algebra for the composition of morphisms and is anti-isomorphic as such with the direct sum...

Building on the work of P.N. Norton, we give combinatorial formulae for two maximal decompositions of the identity into orthogonal idempotents in the 0-Hecke algebra of the symmetric group, CH0(SN ). This construction is compatible with the branching from H0(SN−1) to H0(SN ). Résumé. En s’appuyant sur le travail de P.N. Norton, nous donnons des formules combinatoires pour deux décompositions ma...

In this paper we provide concrete constructions of idempotents to represent typical singular matrices over a given ring as a product of idempotents and apply these factorizations for proving our main results. We generalize works due to Laffey ([12]) and Rao ([3]) to noncommutative setting and fill in the gaps in the original proof of Rao’s main theorems (cf. [3], Theorems 5 and 7 and [4]). We a...

We describe products of arbitrary L, R, and H-classes with the set of idempotents of full transformation semigroups.