اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدConjugacy Limits of the Cartan Subgroup in SL(3,R)
160
0
0.0
(
0
)
تأليف
Arielle Leitner
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A limit group is the limit of a sequence of conjugates of the diagonal Cartan subgroup, C, of SL(3,R). We show C has 5 possible limit groups, up to conjugacy. Each limit group is determined by an equivalence class of nonstandard triangle, and we give a criterion for a sequence of conjugates of C to converge to each of the 5 limit groups.
قيم البحث
اقرأ أيضاً
We give a quadratic lower bound on the dimension of the space of conjugacy classes of subgroups of SL(n,R) that are limits under conjugacy of the diagonal subgroup. We give the first explicit examples of abelian n-1 dimensional subgroups of SL(n,R) w
hich are not such a limit, however all such abelian groups are limits of the diagonal group iff n < 5.
This paper uses work of Haettel to classify all subgroups of PGL(4,R) isomorphic to (R^3 , +), up to conjugacy. We use this to show there are 4 families of generalized cusps up to projective equivalence in dimension 3.
A group $G$ is called subgroup conjugacy separable if for every pair of non-conjugate finitely generated subgroups of $G$, there exists a finite quotient of $G$ where the images of these subgroups are not conjugate. It is proved that the fundamental
group of a hyperbolic 3-manifold (closed or with cusps) is subgroup conjugacy separable.
In this article we describe the summit sets in B_3, the smallest element in a summit set and we compute the Hilbert series corresponding to conjugacy classes.The results will be related to Birman-Menesco classification of knots with braid index three or less than three.
We study the Chabauty compactification of two families of closed subgroups of $SL(n,mathbb{Q}_p)$. The first family is the set of all parahoric subgroups of $SL(n,mathbb{Q}_p)$. Although the Chabauty compactification of parahoric subgroups is well st
udied, we give a different and more geometric proof using various Levi decompositions of $SL(n,mathbb{Q}_p)$. Let $C$ be the subgroup of diagonal matrices in $SL(n, mathbb{Q}_p)$. The second family is the set of all $SL(n,mathbb{Q}_p)$-conjugates of $C$. We give a classification of the Chabauty limits of conjugates of $C$ using the action of $SL(n,mathbb{Q}_p)$ on its associated Bruhat--Tits building and compute all of the limits for $nleq 4$ (up to conjugacy). In contrast, for $ngeq 7$ we prove there are infinitely many $SL(n,mathbb{Q}_p)$-nonconjugate Chabauty limits of conjugates of $C$. Along the way we construct an explicit homeomorphism between the Chabauty compactification in $mathfrak{sl}(n, mathbb{Q}_p)$ of $SL(n,mathbb{Q}_p)$-conjugates of the $p$-adic Lie algebra of $C$ and the Chabauty compactification of $SL(n,mathbb{Q}_p)$-conjugates of $C$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
