Matrix invariants and complete intersections
Glasgow mathematical journal, Tome 32 (1990) no. 2, pp. 227-229

Voir la notice de l'article provenant de la source Cambridge University Press

Consider the vector space of m-tuples of n by n matrices.The linear group GLn(C) acts on Xm, n by simultaneous conjugation. The corresponding ring of polynomial invariantswill be denoted by C(n, m) and is called the ring of matrix invariants of m-tuples of n by n matrices. C. Procesi has shown in [8] that C(n, m) is generated by traces of products of the corresponding generic matrices and, as such, coincides with the center of the trace ring of m generic n by n matrices R (n, m) which is also the ring of equivariant maps from Xm, n to Mn(C).
Bruyn, Lieven le; Teranishi, Yasuo. Matrix invariants and complete intersections. Glasgow mathematical journal, Tome 32 (1990) no. 2, pp. 227-229. doi: 10.1017/S0017089500009265
@article{10_1017_S0017089500009265,
     author = {Bruyn, Lieven le and Teranishi, Yasuo},
     title = {Matrix invariants and complete intersections},
     journal = {Glasgow mathematical journal},
     pages = {227--229},
     year = {1990},
     volume = {32},
     number = {2},
     doi = {10.1017/S0017089500009265},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009265/}
}
TY  - JOUR
AU  - Bruyn, Lieven le
AU  - Teranishi, Yasuo
TI  - Matrix invariants and complete intersections
JO  - Glasgow mathematical journal
PY  - 1990
SP  - 227
EP  - 229
VL  - 32
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009265/
DO  - 10.1017/S0017089500009265
ID  - 10_1017_S0017089500009265
ER  - 
%0 Journal Article
%A Bruyn, Lieven le
%A Teranishi, Yasuo
%T Matrix invariants and complete intersections
%J Glasgow mathematical journal
%D 1990
%P 227-229
%V 32
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500009265/
%R 10.1017/S0017089500009265
%F 10_1017_S0017089500009265

[0] 0.Formanek, E., Invariants and the ring of generic matrices, J. Algebra 89 (1984), 178–223. Google Scholar | DOI

[1] 1.le Bruyn, L., The Artin-Schofield theorem and some applications, Comm. Algebra 14 (1986), 1439–1455. Google Scholar

[2] 2.le Bruyn, L., Trace rings of generic 2 by 2 matrices, Mem. Amer. Math. Soc. 363 (1987). Google Scholar

[3] 3.le Bruyn, L. and Bergh, M. van den, An explicit description of π, Ring theory (Ed. Oystaeyen, F. M. J. van), Lecture Notes in Mathematics No. 1197 (Springer, 1986), 109–113. Google Scholar | DOI

[4] 4.le Bruyn, L. and Bergh, M. van den, Regularity of trace rings of generic matrices, J. Algebra 117 (1988), 19–29. Google Scholar

[5] 5.le Bruyn, L. and Procesi, C., Etale local structure of matrix invariants and concomitants, Algebraic groups, Utrecht 1986 (Ed. Cohen, A. M., Hesselink, W. H., Kallen, W. L. J. van der and Strooker, J. R.), Lecture Notes in Mathematics 1271 (Springer, 1987), 143–175. Google Scholar

[6] 6.le Bruyn, L. and Procesi, C., Semi-simple representations of quivers, Trans. Amer. Math. Soc. to appear. Google Scholar

[7] 7.Procesi, C., Rings with polynomial identities (Marcel Dekker, 1973). Google Scholar

[8] 8.Procesi, C., Invariant theory of n × n matrices, Adv. in Math. 19 (1976), 306–381. Google Scholar

[9] 9.Procesi, C., Computing with 2 × 2 matrices, Algebra 87 (1984), 342–359. Google Scholar

[10] 10.Teranishi, Y., The ring of invariants of matrices, Nagoya Math. J. 104 (1986), 149–161. Google Scholar | DOI

Cité par Sources :