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Sunday, October 11, 2020 | History

5 edition of Varieties of representations of finitely generated groups found in the catalog.

# Varieties of representations of finitely generated groups

## by Alexander Lubotzky

• 245 Want to read
• 40 Currently reading

Published by American Mathematical Society in Providence, R.I., USA .
Written in English

Subjects:
• Representations of groups.,
• Algebraic varieties.,
• Group schemes (Mathematics)

• Edition Notes

Classifications The Physical Object Statement Alexander Lubotzky and Andy R. Magid. Series Memoirs of the American Mathematical Society,, no. 336 Contributions Magid, Andy R. LC Classifications QA3 .A57 no. 336, QA171 .A57 no. 336 Pagination xi, 117 p. ; Number of Pages 117 Open Library OL2540194M ISBN 10 082182337X LC Control Number 85021444

In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination (under the group operation) of finitely many elements of the finite set S and of inverses of such elements.. By definition, every finite group is finitely generated, since S can be taken to be G itself. Every infinite finitely generated group. @article{osti_, title = {Irreducible representations of finitely generated nilpotent groups}, author = {Beloshapka, I V and Gorchinskiy, S O}, abstractNote = {We prove that irreducible complex representations of finitely generated nilpotent groups are monomial if and only if they have finite weight, which was conjectured by Parshin.

This book consists of three parts, rather different in level and purpose: The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and charac- ters. This is a fundamental result, of constant use in mathematics as well as in quantum chemistry or physics/5(3). Representation theory of Lie groups and more generally linear algebraic groups. The representation theory of infinite finitely generated groups is in general mysterious; the object of interest in this case are the character varieties of the group, which are well understood only in very few cases, for example free groups, surface groups and more generally lattices in Lie groups (for example through .

Given a finitely generated group G, the set R(G) of its representations over SL (2, C) can be endowed with the structure of an affine algebraic variety (see [13]), the same holds for the set X(G. In general, the representation zeta function of a finitely generated torsion-free nilpotent group enumerates equivalence classes of representations, called twist-isoclasses.

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### Varieties of representations of finitely generated groups by Alexander Lubotzky Download PDF EPUB FB2

: Varieties of Representations of Finitely Generated Groups (Memoirs of the American Mathematical Society) (): Lubotzky, Alexander, Magid, Andy R.: BooksCited by: Varieties of Representations of Finitely Generated Groups, Issue Volume of American Mathematical Society: Memoirs of the American Mathematical Society Issues of Memoirs Series.

Varieties of representations of finitely generated groups. [Alexander Lubotzky; Andy R Magid] -- The n-dimensional representations, over an algebraically closed characteristic zero field k, of a finitely generated group are parameterized by an affine algebraic variety over k.

Memoirs of the American Mathematical Society Number Alexander Lubotzky and Andy R. Magid Varieties of representations of finitely generated groups Published by the AMERICAN MATHEMATICAL SOCIETY Providence, Rhode Island, USA November • Volume 58 - Number (second of four numbers) MEMOIRS of the American Mathematical Society SUBMISSION.

Varieties of representations of finitely generated groups About this Title. Alexander Lubotzky and Andy R. Magid. Publication: Memoirs of the American Mathematical Society Publication Year Vol Number ISBNs: (print); (online) DOI:   Representation Growth of Finitely Generated Torsion-Free Nilpotent Groups: Methods and Examples | Shannon Ezzat | download | B–OK.

Download books for free. Find books. Notes on Group Theory. This note covers the following topics: Notation for sets and functions, Basic group theory, The Symmetric Group, Group actions, Linear groups, Affine Groups, Projective Groups, Finite linear groups, Abelian Groups, Sylow Theorems and Applications, Solvable and nilpotent groups, p-groups, a second look, Presentations of Groups, Building new groups from old.

Given a finitely generated (fg) group G, the set R(G) of homomorphisms from G to SL 2 C inherits the structure of an algebraic variety known as the representation variety of G in SL 2 C.

This algebraic variety is an invariant of fg presentations of G. Call a group G parafree of rank n if it shares the lower central Varieties of representations of finitely generated groups book with a free group of rank n, and if it is residually nilpotent.

Varieties of algebras are equationally defined classes of algebras, or "primitive classes" in MAL'CEV'S terminology. They made their first explicit appearance in the 's, in Garrett BIRKHOFF'S paper on "The structure of abstract algebras" and B. NEUMANN'S paper "Identical relations in groups I".

For quite some time after this, there is little published evidence that the subject remained. [Pl] V. Platonov, Rings and varieties of representations of finitely generated groups, Topics in Algebra.

Minsk, 4 (), 36–40 (in Russian). zbMATH MathSciNet Google Scholar [Pl-R] V. Platonov and A. Rapinchuk, Algebraic Groups and Number Theory, Academic Press, New York, Representation Theory of Finite Groups and Associative Algebras - Ebook written by Charles W.

Curtis, Irving Reiner. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Representation Theory of Finite Groups and Associative Algebras. Representation varieties of finitely generated groups.

Configuration spaces of elementary geometric objects like arrangements and mechanical linkages. Fundamental groups of Kahler manifolds and smooth algebraic varieties. Manifolds of nonpositive curvature and quasi-isometries. Moduli spaces of representations of finitely generated nilpotent groups naturally arise in the study of algebraic varieties using methods of higher-dimensional adeles.

These moduli spaces are expected to be used in questions related to -functions of varieties over finite fields; for further details, see [. Let $$\\mathfrak {X}(\\Gamma,G)$$ X (Γ, G) be the G-character variety of $$\\Gamma$$ Γ where G is a rank 1 complex affine algebraic group and $$\\Gamma$$ Γ is a finitely presentable discrete group.

We describe an algorithm, which we implement in Mathematica, SageMath, and in Python, that takes a finite presentation for $$\\Gamma$$ Γ and produces a finite presentation of the. Abstract: We study properties of irreducible and completely reducible representations of finitely generated groups Gamma into reductive algebraic groups G in in the context of the geometric invariant theory of the G-action on Hom(Gamma,G) by conjugation.

In particular, we study properties of character varieties, X_G(Gamma)=Hom(Gamma,G)//G. We describe the tangent spaces to.

A finitely generated algebra A in a variety V is called finitely determined in V if there exists a finite V-consistent set of equalities and inequalities in an alphabet containing the generating set of A, which, together with the identities of V, yields all relations and non-relations of sly, if the equational theory of V is recursively enumerable then any finitely determined algebra.

We start with a basic fact about group algebras of p-groups in characteristic p. Theorem Let k be a field of characteristic p and G a p-group.

The regular representation is an indecomposable projective module that is the projective cover of the trivial representation. Every finitely generated. Foreword.- Preface.- Preliminaries.- Tools: Presentations and their Calculus.- Constructions.- Representations and a Theorem of Krasner and Kaloujnine.- The Bieri-Strebel Theorems.- Finitely Generated Metabelian Groups.- An Embedding Theorem for Finitely Generated Metabelian Groups.- Sketch of Proof of Lemma Theorem Details But it should be even stronger.

The group must live in GL_2 of a finitely generated ring. Such groups somehow are close to being free. For example GL_2(Z) is virtually free. Experts will say more. $\endgroup$ – Benjamin Steinberg Jul 23 '12 at The representation space or character variety of a finitely generated group is easy to define but difficult to do explicit computations with.

The fundamental group of a knot can have two interesting representations into PSL2(C) coming from oppositely oriented complete hyperbolic structures.

These two representations lift to give four excellent SL2(C) representations. In this note we prove a counterpart of this result for groups with property A in terms of uniformly bounded representations. A representation π of a group G on a Hilbert space H is said to be uniformly bounded if sup g ∈ G ‖ π g ‖ B (H) finitely generated group equipped with a word length function.Varieties of group representations and splittings of 3-manifolds By MARc CULLER and PETER B.

SHALEN Introduction This paper introduces a new technique in 3-dimensional topology. It is based on the interplay among hyperbolic geometry, the theory of incompressible surfaces, and the structure theory of subgroups of SL2(F), where F is a field.More precisely, we prove local functional equations for the subring zeta functions associated to rings, the subgroup, conjugacy and representation zeta functions of finitely generated, torsion-free nilpotent (or $\mathcal{T}$-)groups, and the normal zeta functions of $\mathcal{T}$-groups of class $2$.