**Contemporary Mathematics**

Volume: 229;
1998;
356 pp;
Softcover

MSC: Primary 14; 16; 17; 81;

Print ISBN: 978-0-8218-0928-0

Product Code: CONM/229

List Price: $96.00

AMS Member Price: $76.80

MAA member Price: $86.40

**Electronic ISBN: 978-0-8218-7820-0
Product Code: CONM/229.E**

List Price: $96.00

AMS Member Price: $76.80

MAA member Price: $86.40

# Trends in the Representation Theory of Finite Dimensional Algebras

Share this page *Edited by *
*Edward L. Green; Birge Huisgen-Zimmermann*

This refereed collection of research papers and survey
articles reflects the interplay of finite-dimensional algebras with
other areas (algebraic geometry, homological algebra, and the theory
of quantum groups). Current trends are presented from the discussions
at the AMS-IMS-SIAM Joint Summer Research Conference at the University of
Washington (Seattle).

The volume features several excellent expository articles which
will introduce the beginning researcher to cutting-edge topics in
representation theory. The book will also provide inspiration to
researchers in related areas, as it includes original papers spanning
a broad spectrum of representation theory.

Features:

- Work outlining significant progress on long-standing open problems.
- Survey articles offering both overviews and introductions to various subfields of the topic.
- Expositions reflecting the interplay between the representation theory of algebras and other fields.

#### Readership

Graduate students and researchers in representation theory of algebras, noetherian rings, Hopf algebras, quantum groups, deformation theory, applications of algebraic geometry and invariant theory to representation theory.

# Table of Contents

## Trends in the Representation Theory of Finite Dimensional Algebras

- Contents vii8 free
- Preface ix10 free
- List of Talks xi12 free
- Postprojective partitions for tilting torsion pairs 116 free
- Derived canonical algebras as one-point extensions 722
- Special biserial algebras and their automorphisms 1732
- Wild subquivers of the Auslander-Reiten quiver of a tame algebra 2944
- Representation theory of noetherian Hopf algebras satisfying a polynomial identity 4964
- Finite representation type and periodic Hochschild (co-)homology 8196
- Introduction 8196
- 1. Results and Examples 8297
- 2. Full Additive Subcategories with Plenty of Projectives 88103
- 3. Functor Categories 92107
- 4. The Auslander-Reiten Structure Theorem 96111
- 5. Exact Frobenius Categories with Enough Projective-Injectives 99114
- 6. Finite Representation Type 102117
- 7. Periodic Hochschild (Co-) Homolog 105120
- References 108123

- The syzygy theorem for monomial algebras 111126
- Algebras whose derived category is tame 117132
- Circular biextensions of tame concealed algebras 129144
- On the distribution of AR-components of restricted Lie algebras 139154
- Compatible deformations 159174
- Directing objects in hereditary categories 169184
- On subcategories associated with tilting modules 181196
- Modules of the highest homological dimension over a Gorenstein ring 193208
- Derived equivalence of graph algebras 201216
- Basic results on wild hereditary algebras 215230
- On minimal approximations of modules 227242
- Serre duality for generalized Auslander regular algebras 237252
- Classifying finite-dimensional semisimple Hopf algebras 265280
- Geometry of modules: Degenerations 281296
- The preprojective algebra of a tame quiver: The irreducible components of the module varieties 293308
- Representation types, Tits reduced quadratic forms and orbit problems for lattices over orders 307322
- Degenerations in module varieties with finitely many orbits 343358