# Product splittings for p-compact groups

Fundamenta Mathematicae (1995)

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

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topDwyer, 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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- [6] W. G. Dwyer and C. W. Wilkerson, The center of a p-compact group, preprint, Notre Dame, 1993.
- [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] H. R. Miller, The Sullivan conjecture on maps from classifying spaces, Ann. of Math. 120 (1984), 39-87. Zbl0552.55014
- [9] J. M. Moller, Rational isomorphisms of p-compact groups, preprint, Matematisk Institut, København, 1994.
- [10] J. M. Moller and D. Notbohm, Centers and finite coverings of finite loop spaces, J. Reine Angew. Math., to appear. Zbl0806.55008
- [11] D. Notbohm, Unstable splittings of classifying spaces of p-compact groups, preprint, Univ. Göttingen, 1994. Zbl0954.55013

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