



LEADER 
02523nmm a2200325 u 4500 
001 
EB001895969 
003 
EBX01000000000000001058975 
005 
00000000000000.0 
007 
cr 
008 
200506  eng 
020 


a 9783030351182

100 
1 

a Assem, Ibrahim

245 
0 
0 
a Basic Representation Theory of Algebras
h Elektronische Ressource
c by Ibrahim Assem, Flávio U. Coelho

250 


a 1st ed. 2020

260 


a Cham
b Springer International Publishing
c 2020, 2020

300 


a X, 311 p. 288 illus
b online resource

505 
0 

a Introduction  Chapter 1: Modules, algebras and quivers  Chapter 2: The radical and almost split sequences  Chapter 3: Constructing almost split sequences  Chapter 4: The Auslander–Reiten quiver of an algebra  Chapter 5: Endomorphism algebras  Chapter 6: Representationfinite algebras  Bibliography  Index

653 


a Associative algebras

653 


a Algebra, Homological

653 


a Category Theory, Homological Algebra

653 


a Associative rings

653 


a Associative Rings and Algebras

700 
1 

a Coelho, Flávio U.
e [author]

041 
0 
7 
a eng
2 ISO 6392

989 


b Springer
a Springer eBooks 2005

490 
0 

a Graduate Texts in Mathematics

028 
5 
0 
a 10.1007/9783030351182

856 
4 
0 
u https://doi.org/10.1007/9783030351182?nosfx=y
x Verlag
3 Volltext

082 
0 

a 512.46

520 


a This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the AuslanderReiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the AuslanderReiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representationfinite algebras, which are now the best understood class of algebras. Intended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course innoncommutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book
