An Ehp Proof of the Lambda Algebra Admissible Monomial Basis
نویسنده
چکیده
The proof follows from relations between Adem relations (4), using what Bousfield calls “pension operators”, i.e. selfmaps of tensor powers which preserve Adem relations. I believe Bousfield had a proof of this sort. Following Mahowald’s suggestion, we’ll give an EHP proof of the basis. Let V be the Z/2 vectorspace with basis {λp : p ≥ −1}. Define e : V → V by e(λp) = λp+1, and define the selfmap D = e⊗1+1⊗e of V ⊗2. We’ll use the original [B-C-K&] symmetric Adem relations, for p ≥ −1, n ≥ 0:
منابع مشابه
On the X basis in the Steenrod algebra
Let $mathcal{A}_p$ be the mod $p$ Steenrod algebra, where $p$ is an odd prime, and let $mathcal{A}$ be the subalgebra $mathcal{A}$ of $mathcal{A}_p$ generated by the Steenrod $p$th powers. We generalize the $X$-basis in $mathcal{A}$ to $mathcal{A}_p$.
متن کاملMonomial Irreducible sln-Modules
In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.
متن کاملCombinatorial Proofs of the Lambda Algebra Basis and Ehp Sequence
Combinatorial proofs are given of the Λ basis and EHP sequence.
متن کاملProof of Dickson’s Lemma Using the ACL2 Theorem Prover via an Explicit Ordinal Mapping
In this paper we present the use of the ACL2 theorem prover to formalize and mechanically check a new proof of Dickson’s lemma about monomial sequences. Dickson’s lemma can be used to establish the termination of Büchberger’s algorithm to find the Gröbner basis of a polynomial ideal. This effort is related to a larger project which aims to develop a mechanically verified computer algebra system.
متن کاملLinking first occurrence polynomials over Fp by Steenrod operations
This paper provides analogues of the results of [16] for odd primes p . It is proved that for certain irreducible representations L(λ) of the full matrix semigroup Mn(Fp), the first occurrence of L(λ) as a composition factor in the polynomial algebra P = Fp[x1, . . . , xn] is linked by a Steenrod operation to the first occurrence of L(λ) as a submodule in P. This operation is given explicitly a...
متن کامل