Dickson Invariants in the Image of the Steenrod Square
نویسنده
چکیده
Let Dn be the Dickson invariant ring of F 2 [X 1 ,. .. , Xn] acted by the general linear group GL(n, F 2). In this paper, we provide an elementary proof of the conjecture by [3]: each element in Dn is in the image of the Steenrod square in F 2
منابع مشابه
A-generators for Ideals in the Dickson Algebra
The Dickson Algebra on q-variables is the algebra of invariants of the action of the mod-2 general linear group on a polynomial algebra in q-variables. We study the structure of certain ideals in this algebra as a module over the Steenrod Algebra A, and develop methods to determine which elements are hit by Steenrod operations. This allows us to display a very small set of A-generators for thes...
متن کاملComputation of Cubical Steenrod Squares
Bitmap images of arbitrary dimension may be formally perceived as unions of m-dimensional boxes aligned with respect to a rectangular grid in R. Cohomology and homology groups are well known topological invariants of such sets. Cohomological operations, such as the cup product, provide higher-order algebraic topological invariants, especially important for digital images of dimension higher tha...
متن کاملGlobal structure of the mod two symmetric algebra , H ∗ ( BO ; F 2 ) , over the Steenrod Algebra
The algebra S of symmetric invariants over the field with two elements is an unstable algebra over the Steenrod algebra A, and is isomorphic to the mod two cohomology of BO , the classifying space for vector bundles. We provide a minimal presentation for S in the category of unstable A-algebras, i.e., minimal generators and minimal relations. From this we produce minimal presentations for vario...
متن کاملNotes on some Distance-Based Invariants for 2-Dimensional Square and Comb Lattices
We present explicit formulae for the eccentric connectivity index and Wiener index of 2-dimensional square and comb lattices with open ends. The formulae for these indices of 2-dimensional square lattices with ends closed at themselves are also derived. The index for closed ends case divided by the same index for open ends case in the limit N →&infin defines a novel quantity we call compression...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000