EUDML

The search session has expired. Please query the service again.

Currently displaying 1 – 5 of 5

Order by Relevance | Title | Year of publication

Ringel-Hall algebras of hereditary pure semisimple coalgebras

Justyna Kosakowska — 2009

Colloquium Mathematicae

We define and investigate Ringel-Hall algebras of coalgebras (usually infinite-dimensional). We extend Ringel's results [Banach Center Publ. 26 (1990) and Adv. Math. 84 (1990)] from finite-dimensional algebras to infinite-dimensional coalgebras.

Sincere posets of finite prinjective type with three maximal elements and their sincere prinjective representations

Justyna Kosakowska — 2002

Colloquium Mathematicae

Assume that K is an arbitrary field. Let (I,⪯) be a poset of finite prinjective type and let KI be the incidence K-algebra of I. A classification of all sincere posets of finite prinjective type with three maximal elements is given in Theorem 2.1. A complete list of such posets consisting of 90 diagrams is presented in Tables 2.2. Moreover, given any sincere poset I of finite prinjective type with three maximal elements, a complete set of pairwise non-isomorphic sincere indecomposable prinjective...

A classification of two-peak sincere posets of finite prinjective type and their sincere prinjective representations

Justyna Kosakowska — 2001

Colloquium Mathematicae

Assume that K is an arbitrary field. Let (I, ⪯) be a two-peak poset of finite prinjective type and let KI be the incidence algebra of I. We study sincere posets I and sincere prinjective modules over KI. The complete set of all sincere two-peak posets of finite prinjective type is given in Theorem 3.1. Moreover, for each such poset I, a complete set of representatives of isomorphism classes of sincere indecomposable prinjective modules over KI is presented in Tables 8.1.

Generic extensions of nilpotent k[T]-modules, monoids of partitions and constant terms of Hall polynomials

Justyna Kosakowska — 2012

Colloquium Mathematicae

We prove that the monoid of generic extensions of finite-dimensional nilpotent k[T]-modules is isomorphic to the monoid of partitions (with addition of partitions). This gives us a simple method for computing generic extensions, by addition of partitions. Moreover we give a combinatorial algorithm that calculates the constant terms of classical Hall polynomials.

Bipartite coalgebras and a reduction functor for coradical square complete coalgebras

Justyna Kosakowska; Daniel Simson — 2008

Colloquium Mathematicae

Let C be a coalgebra over an arbitrary field K. We show that the study of the category C-Comod of left C-comodules reduces to the study of the category of (co)representations of a certain bicomodule, in case C is a bipartite coalgebra or a coradical square complete coalgebra, that is, C = C₁, the second term of the coradical filtration of C. If C = C₁, we associate with C a K-linear functor $ℍ_{C} : C - C o m o d \to H_{C} - C o m o d$ that restricts to a representation equivalence $ℍ_{C} : C - c o m o d \to H_{C} - c o m o d_{s p}^{•}$ , where $H_{C}$ is a coradical square complete hereditary bipartite...

Page 1

Download Results (CSV)

Advanced Search

Formula preview

Currently displaying 1 – 5 of 5

Ringel-Hall algebras of hereditary pure semisimple coalgebras

Sincere posets of finite prinjective type with three maximal elements and their sincere prinjective representations

A classification of two-peak sincere posets of finite prinjective type and their sincere prinjective representations

Generic extensions of nilpotent k[T]-modules, monoids of partitions and constant terms of Hall polynomials

Bipartite coalgebras and a reduction functor for coradical square complete coalgebras