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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| Format: | Online |
| Language: | English |
| Published: |
Open Book Publishers
2025
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| Online Access: | ONIX_20250929T144438_9781805117162_4 |
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| _version_ | 1869516902797148160 |
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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. |
| format | Online |
| id | doab-20.500.12854ir-166818 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Open Book Publishers |
| publisherStr | Open Book Publishers |
| record_format | ojs |
| 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 |