Broline, Crowe and Isaacs have computed the determinant of a matrix associated to a Conway-Coxeter frieze pattern. We generalise their result to the corresponding frieze pattern of cluster variables arising from the Fomin-Zelevinsky cluster algebra of type A. We give a representation-theoretic interpretation of this result in terms of certain configurations of indecomposable objects in the root...

It is proved in this paper that an irreducible module over the non-graded Virasoro-like algebra L, which satisfies a natural condition, is a GHW module or uniformly bounded. Furthermore, we give the complete classification of indecomposable L-modules V = ⊕ m,n∈Z Cvm,n which satisfy Lr,svm,n ⊆ Cvr+m,s+n+1 + Cvr+m,s+n.

We study the equivalence problem of cubic forms. We lower bound its complexity by that of F-algebra isomorphism problem and hence by the graph isomorphism problem (for all fields F). For finite fields we upper bound the complexity of cubic forms by NP∩coAM. We also study the cubic forms obtained from F-algebras and show that they are regular and indecomposable.

We compute all complex structures on indecomposable 6-dimensional real Lie algebras and their equivalence classes. We also give for each of them a global holomorphic chart on the connected simply connected Lie group associated to the real Lie algebra and write down the multiplication in that chart.

We prove that an irreducible quasifinite module over the central extension of the Lie algebra of N × N -matrix differential operators on the circle is either a highest or lowest weight module or else a module of the intermediate series. Furthermore, we give a complete classification of indecomposable uniformly bounded modules.

Let n | m be positive integers with the same prime factors, such that p3 | n for some prime p. We construct a noncrossed product division algebra D with involution ∗, of index m and exponent n, such that D possesses a Baer ordering relative to the involution ∗. Using similar techniques we construct indecomposable division algebras with involution possessing a Baer

It is discussed how stochastic evolutions may be linked to logarithmic conformal field theory. This introduces an extension of the stochastic Löwner evolutions. Based on the existence of a logarithmic null vector in an indecomposable highest-weight module of the Virasoro algebra, the representation theory of the logarithmic conformal field theory is related to entities conserved in mean under t...

In this paper we study the Lie algebras of derivations two-step nilpotent algebras. We obtain a class with trivial center and abelian ideal inner derivations. Among these, relations between complex real case indecomposable Heisenberg Leibniz are thoroughly described. Finally show that every almost derivation algebra one-dimensional commutator ideal, three exceptions, is an derivation.

We study and classify faithfully balanced modules for the algebra of triangular n by matrices more generally Nakayama algebras. The theory extends known results about tilting modules, which are classified binary trees, counted with Catalan numbers. number is a 2-factorial number. Among them n! indecomposable summands, can be interleaved trees or increasing trees.

We investigate a certain class of solvable metric Lie algebras. For this purpose a theory of twofold extensions associated to an orthogonal representation of an abelian Lie algebra is developed. Among other things, we obtain a classification scheme for indecomposable metric Lie algebras with maximal isotropic centre and the classification of metric Lie algebras of index 2.