Product splittings for p-compact groups

W. Dwyer; C. Wilkerson

Fundamenta Mathematicae (1995)

  • Volume: 147, Issue: 3, page 279-300
  • ISSN: 0016-2736

Abstract

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We show that a connected p-compact group with a trivial center is equivalent to a product of simple p-compact groups. More generally, we show that product splittings of any connected p-compact group correspond bijectively to algebraic splittings of the fundamental group of the maximal torus as a module over the Weyl group. These are analogues for p-compact groups of well-known theorems about compact Lie groups.

How to cite

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Dwyer, W., and Wilkerson, C.. "Product splittings for p-compact groups." Fundamenta Mathematicae 147.3 (1995): 279-300. <http://eudml.org/doc/212089>.

@article{Dwyer1995,
abstract = {We show that a connected p-compact group with a trivial center is equivalent to a product of simple p-compact groups. More generally, we show that product splittings of any connected p-compact group correspond bijectively to algebraic splittings of the fundamental group of the maximal torus as a module over the Weyl group. These are analogues for p-compact groups of well-known theorems about compact Lie groups.},
author = {Dwyer, W., Wilkerson, C.},
journal = {Fundamenta Mathematicae},
keywords = {completion of spaces; -compact group; loop space; compact Lie groups; center; torus; maximal torus; Weyl group},
language = {eng},
number = {3},
pages = {279-300},
title = {Product splittings for p-compact groups},
url = {http://eudml.org/doc/212089},
volume = {147},
year = {1995},
}

TY - JOUR
AU - Dwyer, W.
AU - Wilkerson, C.
TI - Product splittings for p-compact groups
JO - Fundamenta Mathematicae
PY - 1995
VL - 147
IS - 3
SP - 279
EP - 300
AB - We show that a connected p-compact group with a trivial center is equivalent to a product of simple p-compact groups. More generally, we show that product splittings of any connected p-compact group correspond bijectively to algebraic splittings of the fundamental group of the maximal torus as a module over the Weyl group. These are analogues for p-compact groups of well-known theorems about compact Lie groups.
LA - eng
KW - completion of spaces; -compact group; loop space; compact Lie groups; center; torus; maximal torus; Weyl group
UR - http://eudml.org/doc/212089
ER -

References

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  1. [1] A. K. Bousfield, The localization of spaces with respect to homology, Topology 14 (1975), 133-150. Zbl0309.55013
  2. [2] A. K. Bousfield and D. M. Kan, Homotopy Limits, Completions and Localizations, Lecture Notes in Math. 304, Springer, Berlin, 1972. Zbl0259.55004
  3. [3] C. Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math. 77 (1955), 778-782. Zbl0065.26103
  4. [4] W. Dwyer, The centralizer decomposition of BG, preprint, Notre Dame, 1994. 
  5. [5] W. G. Dwyer and C. W. Wilkerson, Homotopy fixed point methods for Lie groups and finite loop spaces, Ann. of Math. 139 (1994), 395-442. Zbl0801.55007
  6. [6] W. G. Dwyer and C. W. Wilkerson, The center of a p-compact group, preprint, Notre Dame, 1993. 
  7. [7] J. Lannes, Sur les espaces fonctionnels dont la source est le classifiant d'un p-groupe abélien élémentaire, Publ. Math. Inst. Hautes Études Sci. 75 (1992), 135-244. 
  8. [8] H. R. Miller, The Sullivan conjecture on maps from classifying spaces, Ann. of Math. 120 (1984), 39-87. Zbl0552.55014
  9. [9] J. M. Moller, Rational isomorphisms of p-compact groups, preprint, Matematisk Institut, København, 1994. 
  10. [10] J. M. Moller and D. Notbohm, Centers and finite coverings of finite loop spaces, J. Reine Angew. Math., to appear. Zbl0806.55008
  11. [11] D. Notbohm, Unstable splittings of classifying spaces of p-compact groups, preprint, Univ. Göttingen, 1994. Zbl0954.55013

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