Existence of irreducible ${\mathbb R}$-regular elements in Zariski-dense subgroups
نویسندگان
چکیده
منابع مشابه
Zariski dense surface subgroups in SL(4,Z)
The result of [6] is the existence of an infinite family of Zariski dense surface subgroups of fixed genus inside SL(3,Z); here we exhibit such subgroups inside SL(4,Z) and symplectic groups. In this setting the power of such a result comes in large part from the conclusion that the groups are Zariski dense the existence of surface groups inside SL(4,Z) can be proved fairly easily, since it’s n...
متن کاملZariski dense surface subgroups in SL(3,Z)
The nature of finitely generated infinite index subgroups of SL(3,Z) remains extremely mysterious. It follows from the famous theorem of Tits [12] that free groups abound and, moreover, Zariski dense free groups abound. Less trivially, classical arithmetic considerations (see for example §6.1 of [9]) can be used to construct surface subgroups of SL(3,Z) of every genus ≥ 2. However these are con...
متن کاملBers Slices Are Zariski Dense
Each Bers slice is a holomorphically embedded copy of Teichmüller space within XC(S). While it follows that BY can be locally described as the common zero locus of finitely many analytic functions on XC(S), it is known that the Bers slice is not a locally algebraic set [DK]—this is used to show that W. Thurston’s skinning map is not a constant function [DK]. We prove a stronger result about the...
متن کاملInvariant Measures for Algebraic Actions, Zariski Dense Subgroups and Kazhdan’s Property (t )
Let k be any locally compact non-discrete field. We show that finite invariant measures for k-algebraic actions are obtained only via actions of compact groups. This extends both Borel’s density and fixed point theorems over local fields (for semisimple/solvable groups, resp.). We then prove that for k-algebraic actions, finitely additive finite invariant measures are obtained only via actions ...
متن کاملExistence of solutions for a class of quasilinear Schrödinger equations on R${\mathbb{R}}$
*Correspondence: [email protected] Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, People’s Republic of China Abstract In this paper, we study the existence of nontrivial solution for a class of quasilinear Schrödinger equations in R with the nonlinearity asymptotically linear and, furthermore, the potential indefinite in sign. The tool used in this pa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2003
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2003.v10.n1.a3