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)



An adjoint representation for polynomial algebras

Authors: Stephen A. Mitchell and Robert E. Stong
Journal: Proc. Amer. Math. Soc. 101 (1987), 161-167
MSC: Primary 55R40; Secondary 18G15, 22E45, 57T35
MathSciNet review: 897089
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper shows that a graded polynomial algebra over $ {F_2}$ with Steenrod algebra action possesses an analog of the adjoint representation for the cohomology of the classifying space of a compact connected Lie group.

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

  • [A-W] J. F. Adams and C. W. Wilkerson, Finite $ H$-spaces and algebras over the Steenrod algebra, Ann. of Math. (2) 111 (1980), 95-143. MR 558398 (81h:55006)
  • [B] A. Borel, Sous-groupes commutatifs et torsions des groupes de Lie compacts connexes, Tôhoku Math. J. 13 (1961), 216-240. MR 0147579 (26:5094)
  • [B-H] A. Borel and F. Hirzebruch, Characteristic classes and homogeneous spaces. I, Amer. J. Math. 80 (1958), 458-538. MR 0102800 (21:1586)
  • [B-S] P. Baum and L. Smith, The real cohomology of differentiable fiber bundles, Comment. Math. Helv. 42 (1967), 171-179. MR 0221522 (36:4574)
  • [C-E] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N.J., 1956. MR 0077480 (17:1040e)
  • [H] D. Handel, Thom modules, J. Pure Appl. Algebra 36 (1985), 237-252. MR 790616 (86k:55003)
  • [H-K-R] G. Hochschild, B. Kostant and A. Rosenberg, Differential forms on regular affine algebras, Trans. Amer. Math. Soc. 102 (1962), 383-408. MR 0142598 (26:167)
  • [L-Q] J. L. Loday and D. G. Quillen, Cyclic homology and the Lie algebra homology of matrices, Comment. Math. Helv. 59 (1984), 565-591. MR 780077 (86i:17003)
  • [M] S. A. Mitchell, Finite complexes with $ A\left( n \right)$-free cohomology, Topology 24 (1985), 227-246. MR 793186 (86k:55007)
  • [Q] D. G. Quillen, The spectrum of an equivariant cohomology ring. I, II, Ann. of Math. (2) 94 (1971), 549-602. MR 0298694 (45:7743)
  • [S1] L. Smith, A note on the realization of graded complete intersection algebras by the cohomology of a space, Quart. J. Math. Oxford. 33 (1982), 379-384. MR 668184 (84a:57044a)
  • [S2] -, On the characteristic zero cohomology of the free loop space, Amer. J. Math. 103 (1981), 887-910. MR 630771 (83k:57035)
  • [W] C. W. Wilkerson, Inseparable forms of algebras over the Steenrod algebra, preprint.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55R40, 18G15, 22E45, 57T35

Retrieve articles in all journals with MSC: 55R40, 18G15, 22E45, 57T35

Additional Information

Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society