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Homological methods, representation theory, and cluster algebras

This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands...

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Detalles Bibliográficos
Autores principales: Assem, Ibrahim, Trepode, Sonia
Lenguaje:eng
Publicado: Springer 2018
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-74585-5
http://cds.cern.ch/record/2316196
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author Assem, Ibrahim
Trepode, Sonia
author_facet Assem, Ibrahim
Trepode, Sonia
author_sort Assem, Ibrahim
collection CERN
description This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, while the study of cluster algebras provides representation theory with new objects of study. The six mini-courses comprising this text were delivered March 7–18, 2016 at a CIMPA (Centre International de Mathématiques Pures et Appliquées) research school held at the Universidad Nacional de Mar del Plata, Argentina. This research school was dedicated to the founder of the Argentinian research group in representation theory, M.I. Platzeck.
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spelling cern-23161962021-04-21T18:51:01Zdoi:10.1007/978-3-319-74585-5http://cds.cern.ch/record/2316196engAssem, IbrahimTrepode, SoniaHomological methods, representation theory, and cluster algebrasMathematical Physics and MathematicsThis text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, while the study of cluster algebras provides representation theory with new objects of study. The six mini-courses comprising this text were delivered March 7–18, 2016 at a CIMPA (Centre International de Mathématiques Pures et Appliquées) research school held at the Universidad Nacional de Mar del Plata, Argentina. This research school was dedicated to the founder of the Argentinian research group in representation theory, M.I. Platzeck.Springeroai:cds.cern.ch:23161962018
spellingShingle Mathematical Physics and Mathematics
Assem, Ibrahim
Trepode, Sonia
Homological methods, representation theory, and cluster algebras
title Homological methods, representation theory, and cluster algebras
title_full Homological methods, representation theory, and cluster algebras
title_fullStr Homological methods, representation theory, and cluster algebras
title_full_unstemmed Homological methods, representation theory, and cluster algebras
title_short Homological methods, representation theory, and cluster algebras
title_sort homological methods, representation theory, and cluster algebras
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-74585-5
http://cds.cern.ch/record/2316196
work_keys_str_mv AT assemibrahim homologicalmethodsrepresentationtheoryandclusteralgebras
AT trepodesonia homologicalmethodsrepresentationtheoryandclusteralgebras