UNSTABLE ALGEBRAS OVER AN OPERAD II

被引：0

作者：

Ikonicoff, Sacha ^{[1
]}

机构：

[1] Univ Ottawa, Dept Math & Stat, STEM Complex, 150 Louis Pasteur Pvt, Ottawa, ON K1N 6N5, Canada

来源：

HOMOLOGY HOMOTOPY AND APPLICATIONS | 2024年 / 26卷 / 01期

关键词：

Steenrod algebra; bialgebra; unstable module; operad; POLYNOMIAL ALGEBRAS; STEENROD ALGEBRA; MODULES; CONJECTURE; MAPS;

D O I：

10.4310/HHA.2024.v26.n1.a4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We work over the finite field F-q. We introduce a notion of unstable P-algebra over an operad P. We show that the unstable P-algebra freely generated by an unstable module is itself a free P-algebra under suitable conditions. We introduce a family of 'q-level' operads which allows us to identify unstable modules studied by Brown-Gitler, Miller and Carlsson in terms of free unstable q-level algebras.

引用

页码：37 / 67

页数：31

共 22 条

[1] [Anonymous], 1995, K-Theory, V9, P273
[2] Brown E.H., 1973, Topology, V12, P283
[3] POLYNOMIAL ALGEBRAS OVER THE STEENROD ALGEBRA
CAMPBELL, HEA
SELICK, PS
[J]. COMMENTARII MATHEMATICI HELVETICI, 1990, 65 (02) : 171 - 180
[4] SEGAL,G.B. BURNSIDE RING CONJECTURE FOR (Z/2)K
CARLSSON, G
[J]. TOPOLOGY, 1983, 22 (01) : 83 - 103
[5] Adem-Cartan operads
Chataur, D
Livernet, M
[J]. COMMUNICATIONS IN ALGEBRA, 2005, 33 (11) : 4337 - 4360
[6] A FAMILY OF UNSTABLE STEENROD-MODULES WHICH INCLUDES THOSE OF CARLSSON,G.
DAVIS, DM
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 1985, 35 (03) : 253 - 267
[7] A CLASSIFICATION OF POLYNOMIAL ALGEBRAS AS MODULES OVER THE STEENROD ALGEBRA
DUFLOT, J
KUHN, NJ
WINSTEAD, M
[J]. COMMENTARII MATHEMATICI HELVETICI, 1993, 68 (04) : 622 - 632
[8] Epstein D.B.A., 1962, Cohomology Operations (AM- 50): Lectures by N.E. Steenrod. (AM-50)
[9] Fresse B, 2009, LECT NOTES MATH, V1967, P1
[10] Fresse Benoit, 2017, Mathematical Surveys and Monographs, V217

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