Algebra
On complexity of representations of quivers
Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 841-845.

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.

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

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2019.10.013
Kac, Victor G. 1

1 Department of Mathematics, M.I.T, Cambridge, MA 02139, USA
@article{CRMATH_2019__357_11-12_841_0,
     author = {Kac, Victor G.},
     title = {On complexity of representations of quivers},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {841--845},
     publisher = {Elsevier},
     volume = {357},
     number = {11-12},
     year = {2019},
     doi = {10.1016/j.crma.2019.10.013},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2019.10.013/}
}
TY  - JOUR
AU  - Kac, Victor G.
TI  - On complexity of representations of quivers
JO  - Comptes Rendus. Mathématique
PY  - 2019
SP  - 841
EP  - 845
VL  - 357
IS  - 11-12
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2019.10.013/
DO  - 10.1016/j.crma.2019.10.013
LA  - en
ID  - CRMATH_2019__357_11-12_841_0
ER  - 
%0 Journal Article
%A Kac, Victor G.
%T On complexity of representations of quivers
%J Comptes Rendus. Mathématique
%D 2019
%P 841-845
%V 357
%N 11-12
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2019.10.013/
%R 10.1016/j.crma.2019.10.013
%G en
%F CRMATH_2019__357_11-12_841_0
Kac, Victor G. 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. http://www.numdam.org/articles/10.1016/j.crma.2019.10.013/

[1] Bernstein, I.N.; Gelfand, I.M.; Ponomarev, V.A. Coxeter functors and Gabriel's theorem, Usp. Mat. Nauk, Volume 28 (1973), pp. 17-32

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

[3] Donovan, P.W.; Freislich, M.R. The Representation Theory of Finite Graphs and Associated Algebras, Carleton Math. Lecture Notes, vol. 5, Carleton University, Ottawa, Ontario, Canada, 1973

[4] Gabriel, P. Unzerlegbare Darstellungen. I, Manuscr. Math., Volume 6 (1972), pp. 71-103 (in German, with English summary); correction: Manuscr. Math., 6, 1972, pp. 309

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

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

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

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

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

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

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

Cited by Sources: