We construct new families of examples of (real) Anosov Lie algebras starting with algebraic units. We also give examples of indecomposable Anosov Lie algebras (not a direct sum of proper Lie ideals) of dimension 13 and 16, and we conclude that for every n ≥ 6 with n 6= 7 there exists an indecomposable Anosov Lie algebra of dimension n.

A result of G. Walker and R. Wood states that the space indecomposable elements in degree 2 n -1-n polynomial algebra

In this paper, we classify all irreducible weight modules with finite dimensional weight spaces over the W -algebra W (2, 2). Meanwhile, all indecomposable modules with one dimensional weight spaces over the W -algebra W (2, 2) are also determined.

In this paper, we classify all irreducible weight modules with finite dimensional weight spaces over the W -algebra W (2, 2). Meanwhile, all indecomposable modules with one dimensional weight spaces over the W -algebra W (2, 2) are also determined.

We construct a new class of positive indecomposable maps in the algebra of d × d complex matrices. Each map is uniquely characterized by a cyclic bistochastic matrix. This class generalizes a Choi map for d = 3. It provides a new reach family of indecomposable entanglement witnesses which define important tool for investigating quantum entanglement.

The blob algebra is a finite-dimensional quotient of the Hecke type B which almost always quasi-hereditary. We construct indecomposable tilting modules for over field characteristic 0 in doubly critical case. Every module maximal highest weight either projective or an extension simple by module. Moreover, every submodule weight. conclude that graded Weyl filtration multiplicities this case are ...

A module is called absolutely indecomposable if it is directly indecomposable in every generic extension of the universe. We want to show the existence of large abelian groups that are absolutely indecomposable. This will follow from a more general result about R-modules over a large class of commutative rings R with endomorphism ring R which remains the same when passing to a generic extension...

In this paper we classify indecomposable modules for the Lie algebra of vector fields on a torus that admit a compatible action of the algebra of functions. An important family of such modules is given by spaces of jets of tensor fields. 0. Introduction. In recent years there was a substantial progress in representation theory of infinitedimensional Lie algebras of rank n > 1, toroidal Lie alge...

It is proved that any cluster-tilted algebra defined in the cluster category C(H) has the same representation type as the initial hereditary algebra H . For any valued quiver (Γ,Ω), an injection from the subset PI(Ω) of the cluster category C(Ω) consisting of indecomposable preprojective objects, preinjective objects and the first shifts of indecomposable projective modules to the set of cluste...