Document Zbl 0409.57037

Homotopy equivalent group representations and Picard groups of the Burnside ring and the character ring. (English) Zbl 0409.57037

Manuscr. Math. 26, 179-200 (1978).

Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0409.57037

MSC:

57S15	Compact Lie groups of differentiable transformations
14C22	Picard groups
20C15	Ordinary representations and characters
55Q50	\(J\)-morphism
57S17	Finite transformation groups

Keywords:

Homotopy Equivalent Group Representations; Picard Group; Rational Representation Ring; Burnside Ring

Cite Review PDF

Full Text: DOI EuDML

References:

[1]	Atiyah, M. F. and Tall, D. O.: Group representations, ?-rings and the J-homomorphism. Topology8, 253-297 (1969) · doi:10.1016/0040-9383(69)90015-9
[2]	tom Dieck, T.: The Burnside ring of a compact Lie group. I. Math. Ann.215, 235-250 (1975) · Zbl 0313.57030 · doi:10.1007/BF01343892
[3]	tom Dieck, T.: Homotopy-equivalent group representations. J. f. d. reine u. angew. Math.298, 182-195 (1978) · Zbl 0368.20006
[4]	tom Dieck, T. and Petrie, T.: Geometric modules over the Burnside ring. Invent, math.47, 273-287 (1978) · Zbl 0389.57008 · doi:10.1007/BF01579214
[5]	Hauschild, H.: Äquivariante Whiteheadtorsion. Manuscripta math.26, 63-82 (1978) · Zbl 0402.57031 · doi:10.1007/BF01167967
[6]	Hilton, P. J. and Stammbach, U.: A Course in Homological Algebra. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0238.18006
[7]	Lee, Chung-Nim and Wasserman, A. G.: On the groups JO(G). Mem. Amer. Math. Soc. 159 (1975) · Zbl 0323.55031
[8]	Roquette, P.: Realisierung von Darstellungen endlicher nilpotenter Gruppen. Arch. Math.9, 241-250 (1958) · Zbl 0083.25002 · doi:10.1007/BF01900587
[9]	Segal, G. B.: Permutation representations of finite p-groups. Quart. J. Math. Oxford (2),23, 375-381 (1972) · Zbl 0338.20017 · doi:10.1093/qmath/23.4.375
[10]	Segal, G. B. and James, I. M.: On equivariant homotopy type. Topology · Zbl 0403.57007
[11]	Serre, J.-P.: Représentations linéaires des groupes finis. 2. éd. Paris: Hermann 1971
[12]	Tornehave, J.: Equivariant maps of spheres with conjugate orthogonal actions. Preprint. Aarhus University 1977

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.