Indecomposable invariants of quivers for dimension $(2,\dots,2)$ and maximal paths,~II
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 350-371.

Voir la notice de l'article provenant de la source Math-Net.Ru

An upper bound on degrees of elements of a minimal generating system for invariants of quivers of dimension $(2,\dots,2)$ is established over a field of arbitrary characteristic and its precision is estimated. The proof is based on the reduction to the problem of description of maximal paths satisfying certain condition.
Keywords: representations of quivers, oriented graphs, maximal paths.
Mots-clés : invariants
@article{SEMR_2010_7_a22,
     author = {A. A. Lopatin},
     title = {Indecomposable invariants of quivers for dimension $(2,\dots,2)$ and maximal {paths,~II}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {350--371},
     publisher = {mathdoc},
     volume = {7},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2010_7_a22/}
}
TY  - JOUR
AU  - A. A. Lopatin
TI  - Indecomposable invariants of quivers for dimension $(2,\dots,2)$ and maximal paths,~II
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2010
SP  - 350
EP  - 371
VL  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2010_7_a22/
LA  - en
ID  - SEMR_2010_7_a22
ER  - 
%0 Journal Article
%A A. A. Lopatin
%T Indecomposable invariants of quivers for dimension $(2,\dots,2)$ and maximal paths,~II
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2010
%P 350-371
%V 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2010_7_a22/
%G en
%F SEMR_2010_7_a22
A. A. Lopatin. Indecomposable invariants of quivers for dimension $(2,\dots,2)$ and maximal paths,~II. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 350-371. http://geodesic.mathdoc.fr/item/SEMR_2010_7_a22/

[1] M. Domokos, “Invariants of quivers and wreath products”, Comm. Algebra, 26 (1998), 2807–2819 | DOI | MR | Zbl

[2] M. Domokos, S. G. Kuzmin, A. N. Zubkov, “Rings of matrix invariants in positive characteristic”, J. Pure Appl. Algebra, 176 (2002), 61–80 | DOI | MR | Zbl

[3] S. Donkin, “Invariants of several matrices”, Invent. Math., 110 (1992), 389–401 | DOI | MR | Zbl

[4] S. Donkin, “Polynomial invariants of representations of quivers”, Comment. Math. Helvetici, 69 (1994), 137–141 | DOI | MR | Zbl

[5] P. Gabriel, “Unzerlegbare Darstellungen I”, Manuscr. Math., 6 (1972), 71–103 | DOI | MR | Zbl

[6] Siberian Mathematical Journal, 45:3 (2004), 513–521 | DOI | MR | Zbl

[7] A. A. Lopatin, “The algebra of invariants of $3\times3$ matrices over a field of arbitrary characteristic”, Comm. Algebra, 32:7 (2004), 2863–2883 | DOI | MR | Zbl

[8] A. A. Lopatin, “Relatively free algebras with the identity $x^3=0$”, Comm. Algebra, 33:10 (2005), 3583–3605 | DOI | MR | Zbl

[9] A. A. Lopatin, A. N. Zubkov, “Semi-invariants of mixed representations of quivers”, Transform. Groups, 12:2 (2007), 341–369 | DOI | MR | Zbl

[10] A. A. Lopatin, “Invariants of quivers under the action of classical groups”, J. Algebra, 321 (2009), 1079–1106 | DOI | MR | Zbl

[11] A. A. Lopatin, Indecomposable invariants of quivers for dimension $(2,\ldots,2)$ and maximal paths, Comm. Algebra (to appear) , arXiv: 0704.2411 | MR

[12] A. A. Lopatin, Minimal generating set for semi-invariants of quivers of dimension two, submitted, arXiv: 1004.3083

[13] C. Procesi, “The invariant theory of $n\times n$ matrices”, Adv. Math., 19 (1976), 306–381 | DOI | MR | Zbl

[14] C. Procesi, “Computing with $2\times2$ matrices”, J. Algebra, 87 (1984), 342–359 | DOI | MR | Zbl

[15] Yu. P. Razmyslov, “Trace identities of full matrix algebras over a field of characteristic $0$”, Izv. Akad. Nauk SSSR Ser. Mat., 38:4 (1974), 723–756 (Russian) | MR | Zbl

[16] K. S. Sibirskii, “Algebraic invariants of a system of matrices”, Sibirsk. Mat. Zh., 9:1 (1968), 152–164 (Russian) | MR

[17] A. N. Zubkov, “The Razmyslov-Procesi theorem for quiver representations”, Fundam. Prikl. Mat., 7:2 (2001), 387–421 (Russian) | MR | Zbl