Abstract
Harish-Chandra [6] found that the Tannaka duality theorem almost holds for connected semisimple Lie groups but it does not hold exactly. It remained an open question when the Tannaka duality theorem holds for semisimple Lie groups. In this paper, we answer the question in the fol lowing way.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. Cartier, “Dualité de Tannaka des groupes et algèbres de Lie,” C.R., Paris 242 (1956), 322–325.
C. Chevalley, Theory of Lie Groups I, Princeton Univ. Press.
C. Chevalley, Théorie des Groupes de Lie, t II, Hermann, 1948.
C. Chevalley and S. Eilenberg, “Cohomology theory of Lie groups and Lie algebras,” Trans. A.M.S. 63 (1948), 85–124.
M. Goto, “Faithful representations of Lie groups,” Math. Japonioa 1 (1948), 107–119.
Harish-Chandra, “Lie algebras and the Tannaka duality theorem,” Ann. of Math. 51 (1950), 299–330.
G. Hochschild and G.D. Mostow, “Representations and representative functions of Lie groups,” Ann. of Math. 66 (1957), 495–542.
Y. Matsushima, “Espaces homogènes de Stein des groupes de Lie complexes,” Nagoya Math. J. 16 (1960), 205–218.
M. Sugiura, “Some remarks on duality theorems of Lie groups,” Proc. Japan Academy 43 (1967), 927–931.
T. Tannaka, “Dualität der nicht-kommutativen Gruppen,” Tohoku Math. J. 53 (1938), 1–12.
H. Weyl, “Theorie der Darstellung kontinuierlicher halbeinfacher Gruppen durch lineare Transformationen I, II, III,” Math. Z. 23 (1925), 271–309, 24 (1926), 328–395.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer Science+Business Media New York
About this chapter
Cite this chapter
Sugiura, M. (1981). The Tannaka Duality Theorem for Semisimple Lie Groups and the Unitarian Trick. In: Hano, Ji., Morimoto, A., Murakami, S., Okamoto, K., Ozeki, H. (eds) Manifolds and Lie Groups. Progress in Mathematics, vol 14. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-5987-9_22
Download citation
DOI: https://doi.org/10.1007/978-1-4612-5987-9_22
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-5989-3
Online ISBN: 978-1-4612-5987-9
eBook Packages: Springer Book Archive