Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-16T15:29:13.489Z Has data issue: false hasContentIssue false
  • English
  • Français

Free Lie algebra and lambda-ring structure

Published online by Cambridge University Press:  17 April 2009

Maria Ronco
Maria Ronco
Affiliation:
Depto. de Matemáticas Facultad de Ciencias Exactas y Nat.Universidat de Buenos AiresArgentina
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let R be a graded λ-ring. We extend a well-known formula in the universal ring of Witt vectors by replacing the power operations by the Adams operations. Our method provides us an easy way to compute the inverse image by the symmetric power operators of certain elements of R. As a corollary we get identities, found by Klyachko and Hanlon, in the rings 1 + ℤ[[t]]+ and 1 + Rˆ[[t]]+, where R is the representation ring of the symmetric groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 3 , December 1994 , pp. 373 - 382
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Dress, A. and Siebeneicher, C., ‘The Burnside ring of the infinite cyclic group and its relations to the necklace algebra, λ-ring and the Universal ring of Witt vectors’, Adv. in Math. 78 (1989), 1–41.CrossRefGoogle Scholar
[2]Gerstenhaber, M. and Schack, S., ‘A Hodge type decomposition for commutative algebra homology’, J. Pure Appl. Algebra 48 (1987), 229–247.CrossRefGoogle Scholar
[3]Hanlon, P., ‘The action of Sn on the components of the Hodge decomposition of Hochschild homology’, Michigan Math. J. 37 (1990), 105–124.CrossRefGoogle Scholar
[4]Klyachko, A., ‘Lie elements in the tensor algebra’, Siberian Math. J. 15 (1974), 1296–1304.Google Scholar
[5]Knutson, D., ‘λ-ring and the representation theory of the symmetric groups IV’, Lecture Notes in Mathematics 308 (Springer-Verlag, Berlin, Heidelberg, New York).Google Scholar
[6]Loday, J.-L., ‘Opérations sur l'homologie cyclique des algèbres commutatives’, Invent. Math. 96 (1989), 205–230.CrossRefGoogle Scholar
[7]Metropolis, N. and Rota, G-C., ‘The Cyclotomic identity’, Contemp. Math. 34 (1984), 19–24.CrossRefGoogle Scholar
[8]Kerber, J., ‘The representation theory of the symmetric group’, Encyclopedia of Mathematics (Cambridge University Press, Cambridge New York).Google Scholar