Invariants of modular representations and polynomial algebras over the Steenrod algebra
J. Aguadé
Source: Duke Math. J. Volume 52, Number 2
(1985), 315-327.
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References
[1] J. F. Adams and C. Wilkerson, Finite $H$-spaces and algebras over the Steenrod algebra, Ann. of Math. (2) 111 (1980), no. 1, 95–143.
Mathematical Reviews (MathSciNet): MR81h:55006
Zentralblatt MATH: 0404.55020
Digital Object Identifier: doi:10.2307/1971218
JSTOR: links.jstor.org
[2] J. Aguadé, Realizability of cohomology algebras: a survey, Publ. Sec. Mat. Univ. Autònoma Barcelona 26 (1982), no. 2, 25–68.
Mathematical Reviews (MathSciNet): MR85j:55026
Zentralblatt MATH: 0595.55001
[3] J. Aguadé and L. Smith, Modular cohomology algebras, to appear in Amer. J. Math.
Mathematical Reviews (MathSciNet): MR789653
Zentralblatt MATH: 0568.55004
Digital Object Identifier: doi:10.2307/2374367
JSTOR: links.jstor.org
[4] J. Aguadé, A note on realizing polynomial algebras, Israel J. Math. 38 (1981), no. 1-2, 95–99.
Mathematical Reviews (MathSciNet): MR82g:55018
Zentralblatt MATH: 0462.55006
Digital Object Identifier: doi:10.1007/BF02761852
[5] N. Bourbaki, Elements de mathematique. Fasc. XXXIV. Groupes et algebres de Lie. Chapitre IV: Groupes de Coxeter et systemes de Tits. Chapitre V: Groupes engendres par des reflexions. Chapitre VI: systèmes de racines, Actualites Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968.
Mathematical Reviews (MathSciNet): MR39:1590
Zentralblatt MATH: 0186.33001
[6] C. Broto, Tesina, Universitat Autònoma de Bercelona, 1985.
[7] C. Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math. 77 (1955), 778–782.
Mathematical Reviews (MathSciNet): MR17,345d
Zentralblatt MATH: 0065.26103
Digital Object Identifier: doi:10.2307/2372597
JSTOR: links.jstor.org
[8] A. Clark, On $\pi \sb3$ of finite dimensional $H$-spaces, Ann. of Math. (2) 78 (1963), 193–196.
Mathematical Reviews (MathSciNet): MR27:1956
Zentralblatt MATH: 0121.39803
Digital Object Identifier: doi:10.2307/1970508
[9] A. Clark and J. Ewing, The realization of polynomial algebras as cohomology rings, Pacific J. Math. 50 (1974), 425–434.
Mathematical Reviews (MathSciNet): MR51:4221
Zentralblatt MATH: 0333.55002
Project Euclid: euclid.pjm/1102913229
[10] A. Cohen, Finite complex reflection groups, Ann. Sci. École Norm. Sup. (4) 9 (1976), no. 3, 379–436.
Mathematical Reviews (MathSciNet): MR54:10437
Zentralblatt MATH: 0359.20029
[11] L. E. Dickson, A fundamental system of invariants of the general modular linear group with a solution of the form problem, Trans. Amer. Math. Soc. 12 (1911), no. 1, 75–98.
Mathematical Reviews (MathSciNet): MR1500882
Zentralblatt MATH: 42.0136.01
Digital Object Identifier: doi:10.2307/1988736
JSTOR: links.jstor.org
[12] J. Ewing, Sphere bundles over spheres as loop spaces $\rm mod\ p$, Duke Math. J. 40 (1973), 157–162.
Mathematical Reviews (MathSciNet): MR48:3040
Zentralblatt MATH: 0265.55013
Digital Object Identifier: doi:10.1215/S0012-7094-73-04015-5
Project Euclid: euclid.dmj/1077309567
[13] R. Holzsager, $H$-spaces of category $\leq 2$, Topology 9 (1970), 211–216.
Mathematical Reviews (MathSciNet): MR41:6211
Zentralblatt MATH: 0199.26201
Digital Object Identifier: doi:10.1016/0040-9383(70)90010-8
[14] A. Liulevicius, The factorization of cyclic reduced powers by secondary cohomology operations, Mem. Amer. Math. Soc. No. 42 (1962), 112.
Mathematical Reviews (MathSciNet): MR31:6226
Zentralblatt MATH: 0131.38101
[15] H. Mùi, Modular invariant theory and cohomology algebras of symmetric groups, J. Fac. Sci. U. Tokyo 22 (1975), 319–369.
Zentralblatt MATH: 0335.18010
[16] R. Nakagawa and S. Ochiai, On the dimension of generators of a polynomial algebra over the $\rm mod\ p$ Steenrod algebra, Proc. Japan Acad. 43 (1967), 932–936.
Mathematical Reviews (MathSciNet): MR37:6927
Zentralblatt MATH: 0206.25101
Digital Object Identifier: doi:10.3792/pja/1195521387
Project Euclid: euclid.pja/1195521387
[17] H. Nakajima, Invariants of finite groups generated by pseudoreflections in positive characteristic, Tsukuba J. Math. 3 (1979), no. 1, 109–122.
Mathematical Reviews (MathSciNet): MR82i:20058
Zentralblatt MATH: 0418.20041
[18] H. Nakajima, Modular representations of abelian groups with regular rings of invariants, Nagoya Math. J. 86 (1982), 229–248.
Mathematical Reviews (MathSciNet): MR83i:14038
Zentralblatt MATH: 0443.14005
Project Euclid: euclid.nmj/1118786788
[19] H. Nakajima, Modular representations of $p$-groups with regular rings of invariants, Proc. Japan Acad. Ser. A Math. Sci. 56 (1980), no. 10, 469–473.
Mathematical Reviews (MathSciNet): MR82a:20016
Zentralblatt MATH: 0481.20011
Digital Object Identifier: doi:10.3792/pjaa.56.469
Project Euclid: euclid.pja/1195516652
[20] S. Papastavridis, Polynomial algebras which are modules over the $\rm mod-p$ Steenrod algebra, Bull. Soc. Math. Grèce (N.S.) 17 (1976), 24–27.
Mathematical Reviews (MathSciNet): MR57:14002
Zentralblatt MATH: 0395.55004
[21] J.-P. Serre, Groupes finis d'automorphismes d'anneaux locaux réguliers, Colloque d'Algèbre (Paris, 1967), Exp. 8, Secrétariat mathématique, Paris, 1968, p. 11.
Mathematical Reviews (MathSciNet): MR38:3267
Zentralblatt MATH: 0200.00002
[22] G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canadian J. Math. 6 (1954), 274–304.
Mathematical Reviews (MathSciNet): MR15,600b
Zentralblatt MATH: 0055.14305
[23] L. Smith, Polynomial and related algebras as cohomology rings (report on recent progress), Publ. Sec. Mat. Univ. Autònoma Barcelona 26 (1982), no. 3, 161–197.
Mathematical Reviews (MathSciNet): MR85m:55019
Zentralblatt MATH: 0598.55010
[24] L. Smith and R. M. Switzer, Realizability and nonrealizability of Dickson algebras as cohomology rings, Proc. Amer. Math. Soc. 89 (1983), no. 2, 303–313.
Mathematical Reviews (MathSciNet): MR85e:55036
Zentralblatt MATH: 0532.55019
Digital Object Identifier: doi:10.2307/2044922
[25] L. Smith, The nonrealizability of modular rings of polynomial invariants by the cohomology of a topological space, Proc. Amer. Math. Soc. 86 (1982), no. 2, 339–340.
Mathematical Reviews (MathSciNet): MR83j:55014
Zentralblatt MATH: 0505.55022
Digital Object Identifier: doi:10.2307/2043409
[26] N. Steenrod, Polynomial algebras over the algebra of cohomology operations, H-spaces (Actes Réunion Neuchâtel, 1970), Lecture Notes in Mathematics, Vol. 196, Springer, Berlin, 1971-1970, pp. 85–99.
Mathematical Reviews (MathSciNet): MR44:3316
Zentralblatt MATH: 0222.55025
[27] C. Wilkerson, Some polynomial algebras over the Steenrod algebra $A\sbp$, Bull. Amer. Math. Soc. 79 (1973), 1274–1276 (1974).
Mathematical Reviews (MathSciNet): MR49:3938
Zentralblatt MATH: 0249.55015
Digital Object Identifier: doi:10.1090/S0002-9904-1973-13413-5
Project Euclid: euclid.bams/1183535161
[28] C. Wilkerson, $K$-theory operations in $\rm mod$ $p$ loop spaces, Math. Z. 132 (1973), 29–44.
Mathematical Reviews (MathSciNet): MR48:3051
Zentralblatt MATH: 0249.55017
Digital Object Identifier: doi:10.1007/BF01214031
[29] C. Wilkerson, A primer on the Dickson invariants, Proceedings of the Northwestern Homotopy Theory Conference (Evanston, Ill., 1982), Contemp. Math., vol. 19, Amer. Math. Soc., Providence, RI, 1983, pp. 421–434.
Mathematical Reviews (MathSciNet): MR85c:55017
Zentralblatt MATH: 0525.55013
[30] A. Zabrodsky, On the realization of invariant subgroups of $p*X$, preprint.
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