Comptes Rendus
no. 11-12
Algebra
On complexity of representations of quivers
[Sur la complexité des représentations de carquois]

Présenté par : Michèle Vergne

Victor G. Kac1
1 Department of Mathematics, M.I.T, Cambridge, MA 02139, USA
Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 841-845.

Nous montrons qu'étant donné une représentation de carquois sur un corps fini, on peut vérifier en temps polynomial si elle est absolument indécomposable.

It is shown that, given a representation of a quiver over a finite field, one can check in polynomial time whether it is absolutely indecomposable.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.10.013
Victor G. Kac 1

1 Department of Mathematics, M.I.T, Cambridge, MA 02139, USA 
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Victor G. Kac. On complexity of representations of quivers. Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 841-845. doi : 10.1016/j.crma.2019.10.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.10.013/

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[2] W. Crawley-Boevey; M. Van den Bergh Absolutely indecomposable representations and Kac-Moody Lie algebras, Invent. Math., Volume 155 (2004) no. 3, pp. 537-559 (with an appendix by Hiraku Nakajima)

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[5] T. Hausel Kac's conjecture from Nakajima quiver varieties, Invent. Math., Volume 181 (2010) no. 1, pp. 21-37

[6] T. Hausel; E. Letellier; F. Rodriguez-Villegas Positivity for Kac polynomials and DT-invariants of quivers, Ann. of Math. (2), Volume 177 (2013) no. 3, pp. 1147-1168

[7] V.G. Kac Infinite root systems, representations of graphs and invariant theory, Invent. Math., Volume 56 (1980) no. 1, pp. 57-92

[8] V.G. Kac Infinite root systems, representations of graphs and invariant theory II, J. Algebra, Volume 78 (1982), pp. 141-162

[9] V.G. Kac Root systems, representations of quivers and invariant theory, Montecatini, 1982 (Lecture Notes in Math.), Volume vol. 996, Springer, Berlin (1983), pp. 74-108

[10] V.G. Kac Infinite-Dimensional Lie Algebras, Cambridge University Press, Cambridge, UK, 1990

[11] L.A. Nazarova Representations of quivers of infinite type, Math. USSR Izv., Ser. Mat., Volume 7 (1973), pp. 752-791

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