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Partial flag varieties and preprojective algebras

Christof Geiß, Bernard Leclerc, Jan Schröer (2008)

Annales de l’institut Fourier

Let $Λ$ be a preprojective algebra of type $A, D, E$ , and let $G$ be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories $Sub Q$ for $Q$ an injective $Λ$ -module, and we introduce a mutation operation between complete rigid modules in $Sub Q$ . This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to $G$ .

Path coalgebras of profinite bound quivers, cotensor coalgebras of bound species and locally nilpotent representations

Daniel Simson (2007)

Colloquium Mathematicae

We prove that the study of the category C-Comod of left comodules over a K-coalgebra C reduces to the study of K-linear representations of a quiver with relations if K is an algebraically closed field, and to the study of K-linear representations of a K-species with relations if K is a perfect field. Given a field K and a quiver Q = (Q₀,Q₁), we show that any subcoalgebra C of the path K-coalgebra K◻Q containing $K^{◻} Q ₀ \oplus K^{◻} Q ₁$ is the path coalgebra $K^{◻} (Q,)$ of a profinite bound quiver (Q,), and the category C-Comod...

Peak reductions and waist reflection functors

Daniel Simson (1991)

Fundamenta Mathematicae

Perfect Elements in the Free Modular Lattices.

Vlastimil Dlab, Claus Michael Ringel (1980)

Mathematische Annalen

Periodicity and representation type of modular Lie algebras.

Rolf Farnsteiner (1995)

Journal für die reine und angewandte Mathematik

Piecewise hereditary algebras under field extensions

Jie Li (2021)

Czechoslovak Mathematical Journal

Let $A$ be a finite-dimensional $k$ -algebra and $K / k$ be a finite separable field extension. We prove that $A$ is derived equivalent to a hereditary algebra if and only if so is $A \otimes_{k} K$ .

Polynomial functors over finite fields

Teimuraz Pirashvili (1999/2000)

Séminaire Bourbaki

Polynomial growth trivial extensions of simply connected algebras

Jerzy Nehring, Andrzej Skowroński (1989)

Fundamenta Mathematicae

Polynomial invariants of representations of quivers.

Steven Donkin (1994)

Commentarii mathematici Helvetici

Positivity in coefficient-free rank two cluster algebras.

Dupont, Grégoire (2009)

The Electronic Journal of Combinatorics [electronic only]

Präradikale und Endomorphismenringe von Moduln.

Sigurd Elliger (1975)

Aequationes mathematicae

Preface, Contents, List of Participants

Stanisław Balcerzyk, Tadeusz Józefiak, Jan Krempa, Daniel Simson, Wolfgang Vogel (1990)

Banach Center Publications

Preprojective Components of Wild Tilted Algebras.

Otto Kerner (1988)

Manuscripta mathematica

Preradicals

Ladislav Bican, Pavel Jambor, Tomáš Kepka, Petr Němec (1974)

Commentationes Mathematicae Universitatis Carolinae

Prime and coprime modules

L. Bican, P. Jambor, Tomáš Kepka, P. Němec (1980)

Fundamenta Mathematicae

Primitive Ideals of Certain Noetherian Algebras.

Ronald S. Irvin (1979)

Mathematische Zeitschrift

Projective homomorphisms and extensions of lattices.

Klaus W. Roggenkamp (1971)

Journal für die reine und angewandte Mathematik

Projective purities

Ladislav Bican (1972)

Commentationes Mathematicae Universitatis Carolinae

Projective representations of quivers.

Park, Sangwon (2002)

International Journal of Mathematics and Mathematical Sciences

Projektive Abbildung von Moduln

František Machala (1974)

Czechoslovak Mathematical Journal

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