This paper discusses the twisted conjugacy classes in loop groups. We restrict to classical groups and give some explicit classifications. [ABSTRACT FROM AUTHOR]
In this paper, we show that the boundary $partial Sigma (W,S)$ of a right-angled Coxeter system $(W,S)$ is minimal if and only if $W_{tilde {S}}$ is irreducible, where $W_{tilde {S}}$ is the minimum parabolic subgroup of finite index in $W$. We also provide several applications and remarks. In particular, we show that for a right-angled Coxeter system $(W,S)$, the set ${w^{infty }|win W, o(w)=infty }$ is dense in the boundary $partial Sigma (W,S)$. [ABSTRACT FROM AUTHOR]
This paper gives a description of the relative Brauer group ${rm Br}(E/F)$ when $F$ has characteristic $p$, $[E:F]=p$, and the Galois group ${rm Gal}(E_1/F)$ is solvable, where $E_1$ is the Galois closure of $E$ over $F$. [ABSTRACT FROM AUTHOR]
In this brief paper, we observe that basic results from rational homotopy theory provide formulas for the rational homotopy groups of gauge groups of principal bundles $K to P to B$ in terms of the rational homotopy groups of $K$ and cohomology groups of $B$ alone. [ABSTRACT FROM AUTHOR]
For a given finite-type quiver $varGamma $, we will consider scalar-removed representations $(S_{d}, R_{d}(varGamma ))$, where $S_{d}$ is a direct product of special linear algebraic groups and $R_{d}(varGamma )$ is the representation defined naturally by $varGamma $ and a dimension vector $d$. In this paper, we give a necessary and sufficient condition on $d$ that $R_{d}(varGamma )$ has only finitely many $S_{d}$-orbits. This condition can be paraphrased as a condition concerning lattices of small rank spanned by positive roots of $varGamma $. To determine such scalar-removed representations having only finitely many orbits is very fundamental to the open problem of classification of the so-called semisimple finite prehomogeneous vector spaces. We consider everything over an algebraically closed field of characteristic zero. [ABSTRACT FROM AUTHOR]