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Titlebook: Modular Representation Theory of Finite Groups; Peter Schneider Textbook 2013 Springer-Verlag London 2013 Brauer Correspondence.Burnside R

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发表于 2025-3-21 19:45:54 | 显示全部楼层 |阅读模式
书目名称Modular Representation Theory of Finite Groups
编辑Peter Schneider
视频video
概述Provides a concise introduction to modular representation theory.Is aimed at students at masters level.Compares group theoretic and module theoretic concepts.Includes supplementary material:
图书封面Titlebook: Modular Representation Theory of Finite Groups;  Peter Schneider Textbook 2013 Springer-Verlag London 2013 Brauer Correspondence.Burnside R
描述.Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the ‘semisimple case‘ (for example over the field of complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group..Modular Representation Theory of finite Groups. comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green‘s direct analysis of indecomposable representations. There is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called ‘blocks‘ of the group. Brauer‘s work then establishes correspondences between the blocksof the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple a category a block is by the size and
出版日期Textbook 2013
关键词Brauer Correspondence; Burnside Ring; Cartan-Brauer Triangle; Representation Theory; finite Groups
版次1
doihttps://doi.org/10.1007/978-1-4471-4832-6
isbn_softcover978-1-4471-4831-9
isbn_ebook978-1-4471-4832-6
copyrightSpringer-Verlag London 2013
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https://doi.org/10.1007/978-1-4471-4832-6Brauer Correspondence; Burnside Ring; Cartan-Brauer Triangle; Representation Theory; finite Groups
发表于 2025-3-22 06:05:44 | 显示全部楼层
Peter SchneiderProvides a concise introduction to modular representation theory.Is aimed at students at masters level.Compares group theoretic and module theoretic concepts.Includes supplementary material:
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Textbook 2013 in two distinct flavours. In the ‘semisimple case‘ (for example over the field of complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group..Modular Representation The
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Montgomery Arithmetic over Gaussian Integers,tographic system using Gaussian integers. Such a cryptographic system is presented in [103, 104]. Similarly, a Rabin cryptographic system was previously considered over Gaussian integers in [105, 106]. Moreover, coding applications over Gaussian integers [18, 19, 40, 107–109] could also benefit from
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