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Non-linear Group Actions with Polynomial Invariant Rings and a Structure Theorem for Modular Galois Extensions
Non-linear Group Polynomial Invariant Rings
2010/11/24
Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that...
A group has a planar Cayley complex if and only if it has a VAP-free Cayley graph
planar Cayley complex VAP-free Cayley graph
2010/11/23
We prove that a group has a planar Cayley complex if and only if it has a Cayley graph that can be embedded in the euclidean plane without accumulation points of vertices.
A counterexample for Improved Sobolev Inequalities over the 2-adic group
Sobolev Inequalities the 2-adic group
2010/11/9
On the framework of the 2-adic group Z_2, we study a Sobolev-like inequality where we estimate the L^2 norm by a geometric mean of the BV norm and the Besov space B(-1,\infty,\infty) norm. We first s...
The Freudenthal product and orbits in the Jordan algebra over the exceptional Lie group of type F$_{4(-20)}$
Freudenthal orbits Jordan algebra
2010/11/9
The orbit decomposition is presented for the real form of complex simple Jordan algebra with the automorphism group F$_{4(-20)}$, explicitly, in terms of the cross product and the characteristic polyn...
We construct an extension $E(A,G)$ of a given group $G$ by infinite non-Archimedean words over an discretely ordered abelian group like $Z^n$. This yields an effective and uniform method to study var...
Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras
Yang-Baxter equation six-vertex model dihedral group algebras
2010/4/6
The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutio...
Algebraic Linearization of Dynamics of Calogero Type for any Coxeter Group
Algebraic Linearization Dynamics of Calogero Type Coxeter Group
2010/11/2
Calogero-Moser systems can be generalized for any root system (including the non-crystallographic cases). The algebraic linearization of the generalized Calogero-Moser systems and of their quadratic (...