Introduction to the Representation Theory of Algebras

This book gives a general introduction to the theory of representations of algebras. It starts with examples of classification problems of matrices under linear transformations and explains the three common setups: representation of quivers, modules over algebras and additive functors over certain c...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Barot, Michael (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2015.
Edición:1st ed. 2015.
Temas:
Associative rings.
Associative algebras.
Algebra, Homological.
Universal algebra.
Associative Rings and Algebras.
Category Theory, Homological Algebra.
General Algebraic Systems.
Acceso en línea:Texto Completo

MARC

LEADER 00000nam a22000005i 4500
001 978-3-319-11475-0
003 DE-He213
005 20220116024229.0
007 cr nn 008mamaa
008 141229s2015 sz | s |||| 0|eng d
020 |a 9783319114750  |9 978-3-319-11475-0 
024 7 |a 10.1007/978-3-319-11475-0  |2 doi 
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 Barot, Michael.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Introduction to the Representation Theory of Algebras  |h [electronic resource] /  |c by Michael Barot. 
250 |a 1st ed. 2015. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Springer,  |c 2015. 
300 |a X, 179 p. 109 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 
505 0 |a Matrix Problems -- Representations of Quivers -- Algebras -- Module Categories -- Elements of Homological Algebra -- The Auslander-Reiten Theory -- Knitting -- Combinatorial Invariants -- Indecomposables and Dimensions. 
520 |a This book gives a general introduction to the theory of representations of algebras. It starts with examples of classification problems of matrices under linear transformations and explains the three common setups: representation of quivers, modules over algebras and additive functors over certain categories. The main part is devoted to (i) module categories, presenting the unicity of the decomposition into indecomposable modules, the Auslander-Reiten theory and the technique of knitting; (ii) the use of combinatorial tools such as dimension vectors and integral quadratic forms; and (iii) deeper theorems such as Gabriel's Theorem, the trichotomy and the Theorem of Kac - all accompanied by further examples. Each section includes exercises to facilitate understanding. By keeping the proofs as basic and comprehensible as possible and introducing the three languages at the beginning, this book is suitable for readers from the advanced undergraduate level onwards and enables them to consult related, specific research articles. 
650 0 |a Associative rings. 
650 0 |a Associative algebras. 
650 0 |a Algebra, Homological. 
650 0 |a Universal algebra. 
650 1 4 |a Associative Rings and Algebras. 
650 2 4 |a Category Theory, Homological Algebra. 
650 2 4 |a General Algebraic Systems. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783319114767 
776 0 8 |i Printed edition:  |z 9783319114743 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-3-319-11475-0  |z Texto Completo 
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) 

Ejemplares similares