國立虎尾科技大學 |

Basic Representation Theory of Algebras

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Basic Representation Theory of Algebras/ by Ibrahim Assem, Flávio U. Coelho.
作者:	Assem, Ibrahim.
其他作者:	Coelho, Flávio U.
面頁冊數:	X, 311 p. 288 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Category Theory, Homological Algebra. -
電子資源:	https://doi.org/10.1007/978-3-030-35118-2
ISBN:	9783030351182

Basic Representation Theory of Algebras
Assem, Ibrahim.

Basic Representation Theory of Algebras[electronic resource] /by Ibrahim Assem, Flávio U. Coelho. - 1st ed. 2020. - X, 311 p. 288 illus.online resource. - Graduate Texts in Mathematics,2830072-5285 ;. - Graduate Texts in Mathematics,222.

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: Representation-finite algebras -- Bibliography -- Index.

This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander-Reiten 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 Auslander-Reiten 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 representation-finite 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 in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.

ISBN: 9783030351182

Standard No.: 10.1007/978-3-030-35118-2doiSubjects--Topical Terms:

678397
Category Theory, Homological Algebra.

LC Class. No.: QA251.5

Dewey Class. No.: 512.46

Basic Representation Theory of Algebras
LDR:02788nam a22003975i 4500 001 1024466
003 DE-He213
005 20200706124648.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030351182 $9 978-3-030-35118-2
024 7 $a 10.1007/978-3-030-35118-2 $2 doi
035 $a 978-3-030-35118-2
050 4 $a QA251.5
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.46 $2 23
100 1 $a Assem, Ibrahim. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1203936
245 1 0 $a Basic Representation Theory of Algebras $h [electronic resource] / $c by Ibrahim Assem, Flávio U. Coelho.
250 $a 1st ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a X, 311 p. 288 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Graduate Texts in Mathematics, $x 0072-5285 ; $v 283
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: Representation-finite algebras -- Bibliography -- Index.
520 $a This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander-Reiten 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 Auslander-Reiten 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 representation-finite 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 in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.
650 2 4 $a Category Theory, Homological Algebra. $3 678397
650 1 4 $a Associative Rings and Algebras. $3 672306
650 0 $a Homological algebra. $3 1255326
650 0 $a Category theory (Mathematics). $3 1255325
650 0 $a Rings (Algebra). $3 685051
650 0 $a Associative rings. $3 893564
700 1 $a Coelho, Flávio U. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1320615
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030351175
776 0 8 $i Printed edition: $z 9783030351199
830 0 $a Graduate Texts in Mathematics, $x 0072-5285 ; $v 222 $3 1254915
856 4 0 $u https://doi.org/10.1007/978-3-030-35118-2
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)