Let p be an odd prime. The purpose of the paper is to give a mod p analogue for the Singer invariant-theoretic description of the lambda algebra. In other words, we give an invariant-theoretic interpretation for the homology of the mod p Steenrod algebra A. More precisely, we associate to any left A-moduleM a chain complex Γ⁺ M whose homology is isomorphic to Tor_*^A(Z/p, M). This chain complex is built from the Dickson-Mùi invariants of the general linear group GL(n,Z/p) for n > 0. Particularly, in the case M = Z/p, the complex Γ⁺ = Γ⁺Z/p is dual to the lambda algebra, which is the E₁ term of the Adams spectral sequence for spheres. Notably, we naturalize a little bit Singer's way to define Γ⁺M. In fact, we replace Singer's Γ⁺ M by its image under the so-called total power. Consequently, the action of A on the new Γ⁺ M is diagonal, meanwhile that on Singer's Γ⁺ M is not. Also, the differential of the new Γ⁺ M becomes simpler. This naturalization is valid for p = 2 as well as for p an odd prime. © 1995.

Hung N.H.V., Sum N.

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