Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the realization and classification of cyclic extensions of polynomial algebras over the Steenrod algebra

Authors: Howard Hiller and Larry Smith
Journal: Proc. Amer. Math. Soc. 100 (1987), 731-738
MSC: Primary 55S10
MathSciNet review: 894446
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Suppose $ {{\mathbf{R}}^*}$ is an unstable algebra over the Steenrod algebra of the form $ {{\mathbf{P}}^*}(\sqrt[k]{d})$, where $ {{\mathbf{P}}^*}$ is a polynomial algebra over the Steenrod algebra. If $ {{\mathbf{R}}^*}$ is integrally closed then $ {{\mathbf{R}}^*} = P{(V)^{{G_\mathcal{X}}}}$, where $ C \leqslant GL(V)$ is generated by pseudoreflections and $ {G_\mathcal{X}} = \ker \{ \mathcal{X}:G \to {\mathbf{F}}_p^*\} $ is a character of degree $ k$.

References [Enhancements On Off] (What's this?)

  • [1] J. F. Adams and C. W. Wilkerson, Finite $ H$-spaces and algebras over the Steenrod algebra, Ann. of Math. 78 (1980), 95-143. MR 558398 (81h:55006)
  • [2] N. Bourbaki, Groupes et algèbres de Lie. V. Hermann, Paris, 1968. MR 0240238 (39:1590)
  • [3] C. Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math. 78 (1955), 778-782. MR 0072877 (17:345d)
  • [4] H. Hiller, The geometry of Coxeter groups, Pitman, 1982. MR 649068 (83h:14045)
  • [5] S. Landweber, Dickson invariants and prime ideals invariant under Steenrod operations, Rutgers University Preprint, 1984.
  • [6] R. P. Stanley, Relative invariants of finite groups generated by pseudoreflections, J. Algebra 49 (1977), 134-148. MR 0460484 (57:477)
  • [7] C. W. Wilkerson, Classifying spaces, Steenrod operations and algebraic closure, Topology 16 (1977), 227-237. MR 0442932 (56:1307)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55S10

Retrieve articles in all journals with MSC: 55S10

Additional Information

Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society