Real representations of quivers

Lidia Hügeli; Sverre Smalø

Displaying similar documents to “Real representations of quivers”

On additive functions for stable translation quivers

Grzegorz Bobiński (1999)

Colloquium Mathematicae

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The aim of this note is to give a complete description of the positive additive functions for the stable nonperiodic translation quivers with finitely many orbits. In particular, we show that all positive additive functions on the stable translation quivers of Euclidean type (respectively, of wild type) are periodic, and hence bounded (respectively, are unbounded, and hence nonperiodic).

Semilinear relations and *-representations of deformations of so(3)

Yuriĭ Samoĭlenko, Lyudmila Turowska (1997)

Banach Center Publications

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We study a family of commuting selfadjoint operators $= {(A_{k})}_{k = 1}^{n}$ , which satisfy, together with the operators of the family $= {(B_{j})}_{j = 1}^{n}$ , semilinear relations $⅀_{i} f_{i j} () B_{j} g_{i j} () = h ()$ , ( $f_{i j}$ , $g_{i j}$ , $h_{j} : ℝ^{n} \to ℂ$ are fixed Borel functions). The developed technique is used to investigate representations of deformations of the universal enveloping algebra U(so(3)), in particular, of some real forms of the Fairlie algebra $U_{q}^{'} (s o (3))$ .

Projective representations of generalized symmetric groups.

Morris, Alun O., Jones, Huw I. (2003)

Séminaire Lotharingien de Combinatoire [electronic only]

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Junction type representations of the Temperley-Lieb algebra and associated symmetries.

Doikou, Anastasia, Karaiskos, Nikos (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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On representation theory of quantum $S L_{q} (2)$ groups at roots of unity

Piotr Kondratowicz, Piotr Podleś (1997)

Banach Center Publications

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Irreducible representations of quantum groups $S L_{q} (2)$ (in Woronowicz’ approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the case of q being an odd root of unity. Here we find the irreducible representations for all roots of unity (also of an even degree), as well as describe “the diagonal part” of the tensor product of any two irreducible representations. An example of a not completely reducible representation is given. Non-existence of Haar functional is proved. The corresponding...

Partial flag varieties and preprojective algebras

Christof Geiß, Bernard Leclerc, Jan Schröer (2008)

Annales de l’institut Fourier

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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 $G$ .

The combinatorics of quiver representations

Harm Derksen, Jerzy Weyman (2011)

Annales de l’institut Fourier

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We give a description of faces, of all codimensions, for the cones spanned by the set of weights associated to the rings of semi-invariants of quivers. For a triple flag quiver and its faces of codimension 1 this description reduces to the result of Knutson-Tao-Woodward on the facets of the Klyachko cone. We give new applications to Littlewood-Richardson coefficients, including a product formula for LR-coefficients corresponding to triples of partitions lying on a wall of the Klyachko...

On transitive systems of subspaces in a Hilbert space.

Moskaleva, Yuliya P., Samoĭlenko, Yurii S. (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Representation-finite triangular algebras form an open scheme

Stanisław Kasjan (2003)

Open Mathematics

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Let V be a valuation ring in an algebraically closed field K with the residue field R. Assume that A is a V-order such that the R-algebra Ā obtained from A by reduction modulo the radical of V is triangular and representation-finite. Then the K-algebra KA ≅ A ⊗V is again triangular and representation-finite. It follows by the van den Dries’s test that triangular representation-finite algebras form an open scheme.