We study the Gnedin–Kingman graph, which corresponds to Pieri’s rule for monomial basis {Mλ} in algebra QSym of quasisymmetric functions. The paper contains a detailed announcement results concerning classification indecomposable semifinite harmonic functions on graph. For these functions, we also establish multiplicativity property, is an analog Vershik–Kerov ring theorem.

We classify the Harish-Chandra modules over the higher rank Virasoro and super-Virasoro algebras: It is proved that a Harish-Chandra module, i.e., an irreducible weight module with finite weight multiplicities, over a higher rank Virasoro or super-Virasoro algebra is a module of the intermediate series. As an application, it is also proved that an indecomposable weight module with finite weight...

Tilted algebras, that is endomorphism algebras of tilting modules over a hereditary algebra, have been one of the main objects of study in representation theory of algebras since their introduction by Happel and Ringel [9]. As a generalization, Happel, Reiten and Smalø studied endomorphism algebras of tilting objects of a hereditary abelian category which they call quasi-tilted algebras [8]. We...

Higher degree forms are homogeneous polynomials of d>2, or equivalently symmetric d-linear spaces. This paper is mainly concerned about the algebraic structure centres higher with applications specifically to direct sum decompositions, namely expressing as sums in disjoint sets variables. We show that centre algebra almost every form ground field, consequently all absolutely indecomposable. If ...

Cambrian trees are oriented and labeled trees which fulfill local conditions around each node generalizing the conditions for classical binary search trees. Based on the bijective correspondence between signed permutations and leveled Cambrian trees, we define the Cambrian Hopf algebra generalizing J.-L. Loday and M. Ronco’s algebra on binary trees. We describe combinatorially the products and ...

This paper deals with directly indecomposable direct factors of a directed set.

Let A be a truncated quiver algebra over an algebraically closed field such that any oriented cycle in the ordinary of is zero A. We give number indecomposable direct summands middle term almost split sequence for class Hochschild extension algebras by standard duality module D(A).

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.

Duality maps of finite abelian groups are classified. As a corollary, spin models on finite abelian groups which arise from the solutions of the modular invariance equations are determined as tensor products of indecomposable spin models. We also classify finite abelian groups whose Bose-Mesner algebra can be generated by a spin model.