A phenomenon of reciprocity in the universal Steenrod algebra

Author:
Luciano Lomonaco

Journal:
Trans. Amer. Math. Soc. **330** (1992), 813-821

MSC:
Primary 55S99; Secondary 18G10, 18G15, 55U99

DOI:
https://doi.org/10.1090/S0002-9947-1992-1044963-2

MathSciNet review:
1044963

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Abstract: In this paper we compute the cohomology algebra of certain subalgebras and certain quotients of the universal Steenrod algebra , the algebra of cohomology operations for -ring spectra (see M). We prove that

**[B-S]**A. K. Bousfield, E. B. Curtis, D. M. Kan, D. G. Quillen, D. L. Rector, and J. W. Schlesinger,*The**lower central series and the Adams spectral sequence*, Topology**5**(1966), 331-342. MR**0199862 (33:8002)****[BG]**E. H. Brown and S. Gitler,*A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra*, Topology**12**(1973), 283-295. MR**0391071 (52:11893)****[L]**L. Lomonaco,*Dickson invariants and the universal Steenrod algebra*, Rend. Circ. Mat. Palermo (2)**24**(1990), 429-444. MR**1108226 (92e:55017)****[M]**J. P. May,*A general approach to Steenrod operations*, Lecture Notes in Math., vol. 168, Springer-Verlag, 1970, pp. 153-231. MR**0281196 (43:6915)****[P]**S. B. Priddy,*Koszul resolutions*, Trans. Amer. Math. Soc.**152**(1970), 39-60. MR**0265437 (42:346)****[S]**W. M. Singer,*Invariant theory and the lambda algebra*, Trans. Amer. Math. Soc.**280**(1983), 673-693. MR**716844 (85e:55029)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1992-1044963-2

Keywords:
Universal Steenrod algebra,
Koszul algebras

Article copyright:
© Copyright 1992
American Mathematical Society