Donna Testerman's Books

Linear Algebraic Groups and Finite Groups of Lie Type

By: Gunter Malle,Donna Testerman

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Linear Algebraic Groups and Finite Groups of Lie Type

By: Gunter Malle,Donna Testerman

Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.

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Page Count

324

Publisher

Cambridge University Press

Published Date

ISBN 10

113949953X

ISBN 13

9781139499538

Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

By: Ross Lawther,Donna M. Testerman

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Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

By: Ross Lawther,Donna M. Testerman

Let G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let uEG be unipotent. The authors study the centralizer CG(u), especially its centre Z(CG(u)). They calculate the Lie algebra of Z(CG(u)), in particular determining its dimension; they prove a succession of theorems of increasing generality, the last of which provides a formula for dim Z(CG(u)) in terms of the labelled diagram associated to the conjugacy class containing u.

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Page Count

201

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821847694

ISBN 13

9780821847695

Irreducible Almost Simple Subgroups of Classical Algebraic Groups

By: Timothy C. Burness,Soumaia Ghandour,Claude Marion,Donna M. Testerman

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Irreducible Almost Simple Subgroups of Classical Algebraic Groups

By: Timothy C. Burness,Soumaia Ghandour,Claude Marion,Donna M. Testerman

Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a nontrivial -restricted irreducible tensor indecomposable rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where and is a disconnected almost simple positive-dimensional closed subgroup of acting irreducibly on . Moreover, by combining this result with earlier work, they complete the classification of the irreducible triples where is a simple algebraic group over , and is a maximal closed subgroup of positive dimension.

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Page Count

122

Publisher

American Mathematical Soc.

Published Date

ISBN 10

147041046X

ISBN 13

9781470410469

Multiplicity-free Representations of Algebraic Groups

By: Martin W. Liebeck,Gary M. Seitz,Donna M. Testerman

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Multiplicity-free Representations of Algebraic Groups

By: Martin W. Liebeck,Gary M. Seitz,Donna M. Testerman

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Page Count

282

Publisher

American Mathematical Society

Published Date

ISBN 10

1470469057

ISBN 13

9781470469054

Irreducible Geometric Subgroups of Classical Algebraic Groups

By: Timothy C. Burness,,Soumaïa Ghandour,Donna M. Testerman

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Irreducible Geometric Subgroups of Classical Algebraic Groups

By: Timothy C. Burness,,Soumaïa Ghandour,Donna M. Testerman

Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a non-trivial irreducible tensor-indecomposable -restricted rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where is a disconnected maximal positive-dimensional closed subgroup of preserving a natural geometric structure on .

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Page Count

100

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470414945

ISBN 13

9781470414948

Irreducible Subgroups of Exceptional Algebraic Groups

By: Donna M. Testerman

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Irreducible Subgroups of Exceptional Algebraic Groups

By: Donna M. Testerman

Let [italic]Y be a simply-connected, simple algebraic group of exceptional type, defined over an algebraically closed field [italic]k of prime characteristic [italic]p > 0. The main result describes all semisimple, closed connected subgroups of [italic]Y which act irreducibly on some rational [italic]k[italic]Y module [italic]V. This extends work of Dynkin who obtained a similar classification for algebraically closed fields of characteristic 0. The main result has been combined with work of G. Seitz to obtain a classification of the maximal closed connected subgroups of the classical algebraic groups defined over [italic]k.

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Page Count

198

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821824538

ISBN 13

9780821824535

$A_1$ Subgroups of Exceptional Algebraic Groups

By: Ross Lawther,Donna M. Testerman

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$A_1$ Subgroups of Exceptional Algebraic Groups

By: Ross Lawther,Donna M. Testerman

This book is intended for graduate students and research mathematicians interested in group theory and genralizations

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Page Count

146

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821819666

ISBN 13

9780821819661

Washington County Revisited

By: Donna Akers Warmuth

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Washington County Revisited

By: Donna Akers Warmuth

A companion to Images of America: Washington County, this book, Washington County Revisited, depicts more of the areas rich history. In an attempt to thoroughly cover this county in Virginia, Washington County Revisited explores the history of settlements that were once major community centers, including Lodi, Blackwells Chapel, Rich Valley, Lindell, Bethel, Taylors Valley, Hayters Gap, Clinchburg, and Alvarado. Learn even more of the fascinating history surrounding the railroad towns of Damascus, Glade Spring, and Meadowview. Officially formed in 1776 from Fincastle County, the county was named for Gen. George Washington, who was then serving as commander in chief of the Continental Army. Washington County holds the distinction of being the first geographical region to be named for the first U.S. president. With more than 200 images, Washington County Revisited provides a unique visit to this rural region that once served as a gateway to the West along the Great Wagon Road and saw thousands of settlers and goods pass through to uncharted lands.

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Page Count

132

Publisher

Arcadia Publishing

Published Date

ISBN 10

1439635439

ISBN 13

9781439635438

Group Representation Theory

By: Meinolf Geck

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Group Representation Theory

By: Meinolf Geck

After the pioneering work of Brauer in the middle of the 20th century in the area of the representation theory of groups, many entirely new developments have taken place and the field has grown into a very large field of study. This progress, and the remaining open problems (e.g., the conjectures of Alterin, Dade, Broué, James, etc.) have ensured that group representation theory remains a lively area of research. In this book, the leading researchers in the field contribute a chapter in their field of specialty, namely: Broué (Finite reductive groups and spetses); Carlson (Cohomology and representations of finite groups); Geck (Representations of Hecke algebras); Seitz (Topics in algebraic groups); Kessar and Linckelmann (Fusion systems and blocks); Serre (On finite subgroups of Lie groups); Thévenaz (The classification of endo-permutaion modules); and Webb (Representations and cohomology of categories).

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Page Count

472

Publisher

EPFL Press

Published Date

ISBN 10

0849392438

ISBN 13

9780849392436

Multiplicity-free Representations of Algebraic Groups

By: Martin W. Liebeck,Gary M. Seitz,Donna M. Testerman

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Multiplicity-free Representations of Algebraic Groups

By: Martin W. Liebeck,Gary M. Seitz,Donna M. Testerman

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Page Count

282

Publisher

American Mathematical Society

Published Date

ISBN 10

1470469057

ISBN 13

9781470469054

Linear Algebraic Groups and Finite Groups of Lie Type

By: Gunter Malle,Donna Testerman

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Linear Algebraic Groups and Finite Groups of Lie Type

By: Gunter Malle,Donna Testerman

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Page Count

324

Publisher

Cambridge University Press

Published Date

ISBN 10

113949953X

ISBN 13

9781139499538

Irreducible Subgroups of Exceptional Algebraic Groups

By: Donna M. Testerman

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Irreducible Subgroups of Exceptional Algebraic Groups

By: Donna M. Testerman

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Page Count

198

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821824538

ISBN 13

9780821824535

Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

By: Ross Lawther,Donna M. Testerman

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Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

By: Ross Lawther,Donna M. Testerman

The contents of this book cover notation and preliminary results, reduction of the problem, classical groups, associated cocharacters, the connected centralizer, the Lie algebra of the centre of the centralizer, and much more.

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Page Count

201

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821874152

ISBN 13

9780821874158

Irreducible Geometric Subgroups of Classical Algebraic Groups

By: Timothy C. Burness,,Soumaïa Ghandour,Donna M. Testerman

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Irreducible Geometric Subgroups of Classical Algebraic Groups

By: Timothy C. Burness,,Soumaïa Ghandour,Donna M. Testerman

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Page Count

100

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470414945

ISBN 13

9781470414948

A1 Subgroups of Exceptional Algebraic Groups

By: Ross Lawther,Donna M. Testerman

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A1 Subgroups of Exceptional Algebraic Groups

By: Ross Lawther,Donna M. Testerman

Abstract. Let $G$ be a simple algebraic group of exceptional type over an algebraically closed field of characteristic $p$. Under some mild restrictions on $p$, we classify all conjugacy classes of closed connected subgroups $X$ of type $A_1$; for each such class of subgroups, we also determine the connected centralizer and the composition factors in the action on the Lie algebra ${\mathcal L}(G)$ of $G$. Moreover, we show that ${\mathcal L}(C_G(X))=C_{{\mathcal L}(G)}(X)$ for each subgroup $X$. These results build upon recent work of Liebeck and Seitz, who have provided similar detailed information for closed connected subgroups of rank at least $2$. In addition, for any such subgroup $X$ we identify the unipotent class ${\mathcal C}$ meeting it. Liebeck and Seitz proved that the labelled diagram of $X$, obtained by considering the weights in the action of a maximal torus of $X$ on ${\mathcal L}(G)$, determines the ($\mathrm{Aut}\,G$)-conjugacy class of $X$. We show that in almost all cases the labelled diagram of the class ${\mathcal C}$ may easily be obtained from that of $X$; furthermore, if ${\mathcal C}$ is a conjugacy class of elements of order $p$, we establish the existence of a subgroup $X$ meeting ${\mathcal C}$ and having the same labelled diagram as ${\mathcal C}$.

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Page Count

148

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821863975

ISBN 13

9780821863978

Linear Algebraic Groups and Finite Groups of Lie Type

By: Gunter Malle

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Linear Algebraic Groups and Finite Groups of Lie Type

By: Gunter Malle

The first textbook on the subgroup structure, in particular maximal subgroups, for both algebraic and finite groups of Lie type.

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Page Count

325

Published Date

ISBN 10

1107222001

ISBN 13

9781107222007

Book's by Donna Testerman

Linear Algebraic Groups and Finite Groups of Lie Type

Linear Algebraic Groups and Finite Groups of Lie Type

Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

Irreducible Almost Simple Subgroups of Classical Algebraic Groups

Irreducible Almost Simple Subgroups of Classical Algebraic Groups

Multiplicity-free Representations of Algebraic Groups

Multiplicity-free Representations of Algebraic Groups

Irreducible Geometric Subgroups of Classical Algebraic Groups

Irreducible Geometric Subgroups of Classical Algebraic Groups

Irreducible Subgroups of Exceptional Algebraic Groups

Irreducible Subgroups of Exceptional Algebraic Groups

$A_1$ Subgroups of Exceptional Algebraic Groups

$A_1$ Subgroups of Exceptional Algebraic Groups

Washington County Revisited

Washington County Revisited

Group Representation Theory

Group Representation Theory

Multiplicity-free Representations of Algebraic Groups

Multiplicity-free Representations of Algebraic Groups

Linear Algebraic Groups and Finite Groups of Lie Type

Linear Algebraic Groups and Finite Groups of Lie Type

Irreducible Subgroups of Exceptional Algebraic Groups

Irreducible Subgroups of Exceptional Algebraic Groups

Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

Irreducible Geometric Subgroups of Classical Algebraic Groups

Irreducible Geometric Subgroups of Classical Algebraic Groups

A1 Subgroups of Exceptional Algebraic Groups

A1 Subgroups of Exceptional Algebraic Groups

Linear Algebraic Groups and Finite Groups of Lie Type

Linear Algebraic Groups and Finite Groups of Lie Type

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