A comonadic interpretation of Baues-Ellis homology of crossed modules

We introduce and study a homology theory of crossed modules with coefficients in an abelian crossed module. We discuss the basic properties of these new homology groups and give some applications. We then restrict our attention to the case of integral coefficients. In this case we regain the homology of crossed modules originally defined by Baues and further developed by Ellis. We show that it is an instance of Barr-Beck comonadic homology, so that we may use a result of Everaert and Gran to obtain Hopf formulae in all dimensions.Comment: 16 page

Bazzoni-Glaz Conjecture

In their paper, Bazzoni and Glaz conjecture that the weak global dimension of a Gaussian ring is $0,1$ or $\infty$. In this paper, we prove their conjecture.Comment: arXiv admin note: substantial text overlap with arXiv:1107.044

Schur- and Baer-type theorems for Lie and Leibniz algebras

The aim of this article is to obtain variations on the classical theorems of Schur and Baer on finiteness of commutator subgroups, valid in the contexts of Lie algebras and Leibniz algebras over a field. Using non-abelian tensor products and exterior products, we prove Schur's Theorem for finitely generated Leibniz algebras, both Schur's Theorem and Baer's Theorem for finitely generated Lie algebras, and a version of these theorems for finitely presented Lie algebras