Representation Theory

This volume offers a fresh and modern introduction to one of abstract algebra’s key topics. Guiding readers through the transition between structure theory and representation theory, this textbook explores how algebraic objects like groups and rings act as symmetries of other structures. Using the a...

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Main Author: Jan E., Grabowski
Format: Online
Language:English
Published: Open Book Publishers 2025
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Online Access:ONIX_20250929T144438_9781805117162_4
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author Jan E., Grabowski
author_browse Jan E., Grabowski
author_facet Jan E., Grabowski
author_sort Jan E., Grabowski
collection Directory of Open Access Books
description This volume offers a fresh and modern introduction to one of abstract algebra’s key topics. Guiding readers through the transition between structure theory and representation theory, this textbook explores how algebraic objects like groups and rings act as symmetries of other structures. Using the accessible yet powerful language of category theory, the book reimagines standard approaches to topics such as modules and algebras in a way that unlocks modern treatments of more advanced topics such as quiver representations and even representations of Hopf algebras and categories. Aimed at undergraduate students with prior exposure to linear algebra and basic group theory, the book introduces categories early and uses them throughout, providing a cohesive framework that mirrors current mathematical research. Though technically sophisticated, it also includes examples and exercises designed to develop intuition and understanding. Grabowski’s inclusion of computational tools such as SageMath offers a valuable and traditionally underdeveloped bridge between abstract theory and hands-on exploration. This is a uniquely valuable guide for students ready to stretch their understanding of the subject’s conceptual depth and evolving frontiers.
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institution Directory of Open Access Books
language eng
publishDate 2025
publishDateRange 2025
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spelling doab-20.500.12854ir-1668182025-09-30T05:10:52Z Representation Theory Jan E., Grabowski Representation Theory of Finite Groups Representation Theory of Algebras Representation Theory Advanced Algebra Mathematics Mathematics textbook thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics This volume offers a fresh and modern introduction to one of abstract algebra’s key topics. Guiding readers through the transition between structure theory and representation theory, this textbook explores how algebraic objects like groups and rings act as symmetries of other structures. Using the accessible yet powerful language of category theory, the book reimagines standard approaches to topics such as modules and algebras in a way that unlocks modern treatments of more advanced topics such as quiver representations and even representations of Hopf algebras and categories. Aimed at undergraduate students with prior exposure to linear algebra and basic group theory, the book introduces categories early and uses them throughout, providing a cohesive framework that mirrors current mathematical research. Though technically sophisticated, it also includes examples and exercises designed to develop intuition and understanding. Grabowski’s inclusion of computational tools such as SageMath offers a valuable and traditionally underdeveloped bridge between abstract theory and hands-on exploration. This is a uniquely valuable guide for students ready to stretch their understanding of the subject’s conceptual depth and evolving frontiers. 2025-09-30T05:10:51Z 2025-09-30T05:10:51Z 2025-09-29T12:47:25Z 2025 book ONIX_20250929T144438_9781805117162_4 https://library.oapen.org/handle/20.500.12657/106167 9781805117162 9781805117148 9781805117155 https://directory.doabooks.org/handle/20.500.12854/166818 eng open access image/jpeg Attribution-NonCommercial 4.0 International https://library.oapen.org/bitstream/20.500.12657/106167/1/9781805117162.pdf Open Book Publishers Open Book Publishers 10.11647/OBP.0492 10.11647/OBP.0492 b014b543-78bd-4c3b-bc71-b68e2ac855b9 9781805117162 9781805117148 9781805117155 Open Book Publishers 233 Cambridge, UK open access
spellingShingle Representation Theory of Finite Groups
Representation Theory of Algebras
Representation Theory
Advanced Algebra
Mathematics
Mathematics textbook
thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra
thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis
thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics
thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics
Jan E., Grabowski
Representation Theory
title Representation Theory
title_full Representation Theory
title_fullStr Representation Theory
title_full_unstemmed Representation Theory
title_short Representation Theory
title_sort representation theory
topic Representation Theory of Finite Groups
Representation Theory of Algebras
Representation Theory
Advanced Algebra
Mathematics
Mathematics textbook
thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra
thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis
thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics
thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics
topic_facet Representation Theory of Finite Groups
Representation Theory of Algebras
Representation Theory
Advanced Algebra
Mathematics
Mathematics textbook
thema EDItEUR::P Mathematics and Science::PB Mathematics::PBF Algebra
thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis
thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics
thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics
url ONIX_20250929T144438_9781805117162_4
work_keys_str_mv AT janegrabowski representationtheory