3 edition of **Discrete subgroups of Lie groups and applications to moduli** found in the catalog.

Discrete subgroups of Lie groups and applications to moduli

International Colloquium on Discrete Subgroups of Lie Groups and Applications to Moduli Bombay 1973.

- 195 Want to read
- 3 Currently reading

Published
**1975**
by Published for the Tata Institute of Fundamental Research, Bombay [by] Oxford University Press in Bombay, New York
.

Written in English

- Lie groups -- Congresses.,
- Modular groups -- Congresses.

**Edition Notes**

Includes bibliographical references.

Series | Tata Institute of Fundamental Research. Studies in mathematics ; 7, Studies in mathematics (Tata Institute of Fundamental Research) ;, 7. |

Contributions | Baily, Walter L., Tata Institute of Fundamental Research. |

Classifications | |
---|---|

LC Classifications | QA387 .I57 1973 |

The Physical Object | |

Pagination | vi, 348 p. ; |

Number of Pages | 348 |

ID Numbers | |

Open Library | OL4930375M |

ISBN 10 | 019560525X |

LC Control Number | 76357062 |

Properties. Since topological groups are homogeneous, one need only look at a single point to determine if the topological group is particular, a topological group is discrete if and only if the singleton containing the identity is an open set.. A discrete group is the same thing as a zero-dimensional Lie group (uncountable discrete groups are not second-countable so authors . Maximal Operators Associated to Discrete Subgroups of Nilpotent Lie Groups by Akos Magyar, Elias M. Stein, Stephen Wainger §1. Introduction and statement of main theorem The purpose of this paper is to prove a maximal theorem for averages taken over suitable discrete sub-varieties of nilpotent Lie groups.

In this chapter, we study one of the central tools in Lie theory: the matrix exponential function. This function has various applications in the structure theory of matrix groups. Abstract. Discrete groups of motions of spaces of constant curvature, as well as other groups that can be regarded as such (although they may be defined differently), arise naturally in different areas of mathematics and its by:

ON DISCRETE SUBGROUPS OF LIE GROUPS (II) BY ANDRE WEIL (Received October 2, ) 1. This is a continuation of my paper [7] with the same title, which will be referred to as D', and which has to be supplemented in the manner described below in Appendix I. Indeed, the present paper is nothing else. To understand better the structures and applications of discrete subgroups of Lie groups and locally symmetric spaces, an instructional conference titled Geom-etry, Topology and Analysis of Locally Symmetric Spaces and Discrete Groups was held from July 17 to August 4, at the Morningside Center of Mathematics in Beijing.

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International Colloquium on Discrete Subgroups of Lie Groups and Applications to Moduli ( Bombay). Discrete subgroups of Lie groups and applications to moduli. Bombay ; New York: Published for the Tata Institute of Fundamental Research, Bombay [by] Oxford University Press, (OCoLC) Material Type.

Discrete subgroups of Lie groups and applications to moduli: papers presented at the Bombay Colloquium,by Baily [et al.].

Volume 7 of Tata Institute of fundamental research studies in mathematics Tata Institute of Fundamental Research Volume 7 of Studies in mathematics. Discrete subgroups of Lie groups and applications to moduli: Papers presented at the Bombay Colloquium,by Baily [et al.] (Tata Institute of Fundamental Research.

Studies in mathematics ; 7) Paperback – January 1, Format: Paperback. Lectures On Discrete Subgroups Of Lie Groups By G.D. Mostow Notes by Gopal Prasad No part of this book may be reproduced in any form by print, microﬁlm or any other means with-out written permission form the Tata Institute of Fundamental Research, Colaba, Bombay 5.

Tata Institute of Fundamental Research, Bombay By looking at these examples I realized what I should have known long time ago, namely that infinite permutation group (with Dynkin diagram infinite line with integer nodes) is virtually simple.

However, I do not believe one can use this technique to construct simple discrete subgroups of Lie groups. $\endgroup$ – Misha Mar 8 '12 at This book originated from a course of lectures given at Yale University during and a more elaborate one, the next year, at the Tata Institute of Fundamental Research.

Its aim is to present a detailed ac count of some of the recent work on the geometric aspects of the theory of discrete subgroups of Lie by: Its aim is to present a detailed ac count of some of the recent work on the geometric aspects of the theory of discrete subgroups of Lie groups.

Our interest, by and large, is in a special class of discrete subgroups of Lie groups, viz., lattices (by a lattice in a locally compact group G, we mean a discrete subgroup H such that the homogeneous 5/5(1). The present book is devoted to lattices, i.e.

discrete subgroups of finite covolume, in semi-simple Lie groups. By "Lie groups" we not only mean real Lie groups, but also the sets of k-rational points of algebraic groups over local fields k and their direct products. Our results can be applied to the theory of algebraic groups over global fields.

The Paperback of the Discrete Subgroups of Lie Groups by Madabusi S. Raghunathan at Barnes & Noble. FREE Shipping on $35 or more. Due to COVID, orders may be delayed. Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange. Discrete subgroups have played a central role throughout the development of numerous mathematical disciplines. Discontinuous group actions and the study of fundamental regions are of utmost importance to modern geometry. Flows and dynamical systems on homogeneous spaces have found a wide range of applications, and of course number theory without discrete.

Fuchsian groups are, by definition, discrete subgroups of the isometry group of the hyperbolic plane. A Fuchsian group that preserves orientation and acts on the upper half-plane model of the hyperbolic plane is a discrete subgroup of the Lie group PSL(2, R), the group of orientation preserving isometries of the upper half-plane model of the.

DISCRETE SUBGROUPS OF LIE GROUPS We are led therefore to ask whether there always exist discrete subgroups P in a Lie group G such that G/P is compact. Consider the example G = SL(2, R). Here there are three distinctly different methods of constructing such a subgroup P, an analytic, a geometric, and an arithmetic by: 7.

ON DISCRETE SUBGROUPS OF LIE GROUPS BY ANDRt WEIL (Received February 1, ) 1. Let G be a topological group and F an arbitrary group; one may think of F as being provided with the discrete topology.

Consider the space G(" of all mappings of F into G; this is the same as the product HIy FGy, where G, is the same as G for every / e F, and will. Printed in Great Britain DISCRETE UNIFORM SUBGROUPS OF LIE GROUPS T. Wu (Received 11 April ; revised 20 June ) LET G be a topological group.

A closed subgroup H of G is a uniform subgroup if the homogeneous space G/ H is compact. In this note, we shall study the relation between discrete uniform subgroups and the radicals or Cited by: 1.

In Lie theory and related areas of mathematics, a lattice in a locally compact group is a discrete subgroup with the property that the quotient space has finite invariant the special case of subgroups of R n, this amounts to the usual geometric notion of a lattice as a periodic subset of points, and both the algebraic structure of lattices and the geometry of the space of all.

Discrete subgroups of solvable Lie groups have been fairly thoroughly studied, but the results are less complete than those obtained for nilpotent groups. Any lattice in a solvable Lie group is a uniform discrete subgroup. Ihara, Yasutaka (), "On modular curves over finite fields", in Baily, Walter L.

(ed.), Discrete subgroups of Lie groups and applications to moduli (Internat. Colloq., Colloq., Bombay, ), Tata Institute of Fundamental Research Studies in Mathematics, 7, Oxford University Press, pp. –, ISBNMR Here is the abstract: When does Borel's theorem on free subgroups of semisimple groups generalize to other groups.

We initiate a systematic study of this question and find positive and negative answers for it. In particular, we fully classify fundamental groups of surfaces and von Dyck groups that satisfy Borel's theorem. Abstract. A locally compact group G is said to be approximated by discrete subgroups (in the sense of Tôyama) if there is a sequence of discrete subgroups of G that converges to G in the Chabauty topology (or equivalently, in the Vietoris topology).

The notion of approximation of Lie groups by discrete subgroups was introduced by Tôyama in Kodai Math. Cited by: 1. Discrete Subgroups of Semisimple Lie Group. its moduli space is a Shimura variety of `magic' type. In all other cases a quantum-consistent special K\"ahler geometry is either an arithmetic.Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

It only takes a minute to sign up. Embedded Lie subgroups are closed. Ask Question Asked 5 years, Closures of one-parameter subgroups of lie groups. 1.Dynamics in the study of discrete subgroups of Lie groups Rafael Potrie CMAT-UniversidaddelaRepublica VCLAM-Barranquilla [email protected] July RafaelPotrie (UdelaR) Dynamicsand discretesubgroups ofmatrices July 1/25File Size: KB.