A skew lattice is a noncommutative associative analogue of a lattice and as such may be viewed both as an algebraic object and as a geometric object. Whereas recent papers on skew lattices primarily treated algebraic aspects of skew lattices, this article investigates their intrinsic geometry. This geometry is obtained by considering how the coset geometries of the maximal primitive subalgebras...

A non-erasing morphism σ is said to be recognizable on x if there exists ` such that, for each m ∈ Cσ(x), m′ ∈ Z, y[m−`,m+`) = y[m′−`,m′+`) implies that m′ ∈ Cσ(x), with y = σ(x). Is the Thue-Morse substitution σ : a 7→ ab, b 7→ ba recognizable on σ∞(a)? Same question for the Fibonacci substitution τ : a 7→ ab, b 7→ a. Let σ be a primitive morphism that is recognizable on some x and injective o...

A large class of MDS linear codes is constructed. These are endowed with an efficient decoding algorithm. Both the definition and design their algorithm only require from Linear Algebra methods, making them fully accessible for everyone. Thus, first part paper develops a direct presentation by means parity-check matrices, rests upon matrix maps manipulations. The somewhat more sophisticated mat...

For V a vector space over a field, or more generally, over a division ring, it is well-known that every x ∈ End(V ) has an inner inverse; that is, that there exists y ∈ End(V ) satisfying xyx = x. We show here that a large class of such x have inner inverses y that satisfy with x an infinite family of additional monoid relations, making the monoid generated by x and y what is known as an invers...

Let g be a Lie algebra over a field F of characteristic zero, let C be a certain tensor category of representations of g, and C a certain category of duals. In [M 4] we associated to C and C by a Tannaka reconstruction a monoid M with a coordinate ring F [M ] of matrix coefficients, as well as a Lie algebra Lie(M). We interpreted the Tannaka monoid M algebraic geometrically as a weak algebraic ...