Excess and conjugation in the Steenrod algebra
نویسندگان
چکیده
منابع مشابه
On excess filtration on the Steenrod algebra
The theory of unstable modules over the Steenrod algebra has been developed by many researchers and has various geometric applications. (See Schwartz [6] and its references.) It was so successful that it might be interesting to consider the structure of the Steenrod algebra which enable us to define the notion of unstable modules. Let us call the filtration on the Steenrod algebra defined from ...
متن کاملInvariant elements in the dual Steenrod algebra
In this paper, we investigate the invariant elements of the dual mod $p$ Steenrod subalgebra ${mathcal{A}_p}^*$ under the conjugation map $chi$ and give bounds on the dimensions of $(chi-1)({mathcal{A}_p}^*)_d$, where $({mathcal{A}_p}^*)_d$ is the dimension of ${mathcal{A}_p}^*$ in degree $d$.
متن کاملOn 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 کاملPolynomial Modules over the Steenrod Algebra and Conjugation in the Milnor Basis
Let Ps = F2 [x1, . . . , xs] be the mod 2 cohomology of the s-fold product of RP∞ with the usual structure as a module over the Steenrod algebra. A monomial in Ps is said to be hit if it is in the image of the action A ⊗ Ps → Ps where A is the augmentation ideal of A. We extend a result of Wood to determine a new family of hit monomials in Ps. We then use similar methods to obtain a generalizat...
متن کاملNilpotence in the Steenrod Algebra
While all of the relations in the Steenrod algebra, A, can be deduced in principle from the Adem relations, in practice, it is extremely difficult to determine whether a given polynomial of elements in A is zero for all but the most elementary cases. In his original paper [Mi] Milnor states “It would be interesting to discover a complete set of relations between the given generators of A”. In p...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1979
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1979-0534410-8