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.
Accepté le :
Publié le :
@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 -
Kac, Victor G. On complexity of representations of quivers. Comptes Rendus. Mathématique, Tome 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] Coxeter functors and Gabriel's theorem, Usp. Mat. Nauk, Volume 28 (1973), pp. 17-32
[2] 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] The Representation Theory of Finite Graphs and Associated Algebras, Carleton Math. Lecture Notes, vol. 5, Carleton University, Ottawa, Ontario, Canada, 1973
[4] Unzerlegbare Darstellungen. I, Manuscr. Math., Volume 6 (1972), pp. 71-103 (in German, with English summary); correction: Manuscr. Math., 6, 1972, pp. 309
[5] Kac's conjecture from Nakajima quiver varieties, Invent. Math., Volume 181 (2010) no. 1, pp. 21-37
[6] Positivity for Kac polynomials and DT-invariants of quivers, Ann. of Math. (2), Volume 177 (2013) no. 3, pp. 1147-1168
[7] Infinite root systems, representations of graphs and invariant theory, Invent. Math., Volume 56 (1980) no. 1, pp. 57-92
[8] Infinite root systems, representations of graphs and invariant theory II, J. Algebra, Volume 78 (1982), pp. 141-162
[9] Root systems, representations of quivers and invariant theory, Montecatini, 1982 (Lecture Notes in Math.), Volume vol. 996, Springer, Berlin (1983), pp. 74-108
[10] Infinite-Dimensional Lie Algebras, Cambridge University Press, Cambridge, UK, 1990
[11] Representations of quivers of infinite type, Math. USSR Izv., Ser. Mat., Volume 7 (1973), pp. 752-791
Cité par Sources :