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Noncommutative classical invariant theory

Published online by Cambridge University Press:  22 January 2016

Yasuo Teranishi*
Affiliation:
Department of Mathematics, Faculty of Science, Nagoya University, Chikusa-ku, Nagoya 464, Japan
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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
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), 189214.Google Scholar
[2] Dicks, W. and Formanek, E., Poincaré series and a problem of S. Montgomery, Linear and Multilinear Algebra, 12 (1982), 2130.Google Scholar
[3] Kharchenko, V. K., Algebra of invariants of free algebras, Algebras i Logika, 17 (1978), 478487 (in Russian); English translation: Algebra and Logic, 17 (1978), 316321.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), 115.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