Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T09:54:39.757Z Has data issue: false hasContentIssue false
  • English
  • Français

Noncommutative classical invariant theory

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.

Let K be a field of characteristic zero, V a finite dimensional vector space and G a subgroup of GL(V). The action of G on V is extended to the symmetric algebra on V over K,

and the tensor algebra on V over K,

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 112 , December 1988 , pp. 153 - 169
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

References

[1] Almkvist, G., Dicks, W. and Formanek, E., Hilbert series of fixed free algebra and noncommutative classical invariant theory, J. Algebra, 93 (1985), 189–214.Google Scholar
[2] Dicks, W. and Formanek, E., Poincaré series and a problem of S. Montgomery, Linear and Multilinear Algebra, 12 (1982), 21–30.Google Scholar
[3] Kharchenko, V. K., Algebra of invariants of free algebras, Algebras i Logika, 17 (1978), 478–487 (in Russian); English translation: Algebra and Logic, 17 (1978), 316–321.Google Scholar
[4] Lane, D. R., Free algebras of rank two and their automorphisms, Ph.D. thesis, Betford College, London, 1976.Google Scholar
[5] Macdonald, I. G., Symmetric Functions and Hall Polynomials, Oxford University Press, Clarendon, Oxford, 1979.Google Scholar
[6] Sato, M. and Kimura, T., A Classification of irreducible prehomogeneous vector spaces, Nagoya Math. J., 65 (1977), 1–15.Google Scholar
[7] Schur, I., Vorlesungen uver Invariantentheores, Springer-Verlag, Berlin Heidelberg, New York, 1968.Google Scholar
[8] Stanley, R., Combinatorics and Commutative Algebra, Birkhauser, Boston Basel Stuttgalt, 1983.Google Scholar
[9] Weyl, H., The Classical Groups, Princeton University Press, Princeton, New Jersey, 1946.Google Scholar