Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-03T01:24:50.331Z Has data issue: false hasContentIssue false
  • English
  • Français

The Hilbert series of rings of matrix concomitants

Published online by Cambridge University Press:  22 January 2016

Yasuo Teranishi
Yasuo Teranishi*
Affiliation:
Department of Mathematics, Faculty of Science, Nagoya University, Chikusa-ku, Nagoya 464, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Throughout this paper, K will be a field of characteristic zero. Let K ‹x1,…, xm › be the K-algebra in m variables x1…, xm and Im, n the T-ideal consisting of all polynomial identities satisfied by m n by n matrices. The ring R(n, m) = K ‹x1,…, xm ›/Im, n is called the ring of m generic n by n matrices.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 111 , September 1988 , pp. 143 - 156
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

References

[F1] Formanek, E., Invariants and the trace ring of generic matrices, J. Algebra, 89 (1984),178–223.CrossRefGoogle Scholar
[F2] Formanek, E., The functional equation for character series associated to n by n matrices, Trans. Amer. Math. Soc., 295 (1986).Google Scholar
[F-H-L] Formanek, , Halpin, , Li, , The Poincare series of the ring of 2 × 2 generic matrices, J. Algebra, 69 (1981), 105–112.CrossRefGoogle Scholar
[H-R] Hochster, M. and Roverts, J. L., Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay, Adv. in Math., 13 (1974), 115–175.CrossRefGoogle Scholar
[H] Hilbert, D., Uber die vollen Invariantensysteme, Math. Ann., 42 (1893), 313–373.CrossRefGoogle Scholar
[L1] Bruyn, Le, Functional equation of Poincare series of trace rings of generic 2 × 2-matrices, Israel J. Math.Google Scholar
[L2] Bruyn, Le, Trace rings of generic 2 by 2 matrices, Mem. Amer. Math. Soc., to appear.Google Scholar
[L-V] Bruyn, Le and Bergh, Van den, An explicit description of T 3, 2 Lecture Notes in Math., 1197, Springer (1986), 109–113.Google Scholar
[P1] Procesi, C., The invariant theory of n × n matrices, Adv. in Math., 19 (1976), 306–381.CrossRefGoogle Scholar
[P2] Procesi, C., Computing with 2 by 2 matrices, J. Algebra, 87 (1984), 342–359.CrossRefGoogle Scholar
[S] Stanley, R., Combinatrics and commutative algebra, Birkhauser (1983).CrossRefGoogle Scholar
[T1] Teranishi, Y., Linear diophantine equations and invariant theory of matrices, Adv. Stud, in Pure Math., 11 (1987), 259–275.CrossRefGoogle Scholar
[T2] Teranishi, Y., The ring of invariants of matrices, Nagoya Math. J., 104 (1986), 149–161.CrossRefGoogle Scholar