Titlebook: Algebras and Representation Theory; Karin Erdmann,Thorsten Holm Textbook 2018 Springer Nature Switzerland AG 2018 MSC (2010) 16-XX, 16G10,

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CHYME

Karin Erdmann,Thorsten HolmOffers an elementary introduction that includes more advanced topics such as Gabriel’s theorem on quivers.Based on the authors’ extensive undergraduate teaching experience.Provides numerous worked exa

TATE

tendinitis

反話

https://doi.org/10.1057/9781137343215tion. Perhaps the most elementary way to think of modules is to view them as generalizations of vector spaces, where the role of scalars is played by elements in an algebra, or more generally, in a ring. We introduce many examples, and study the fundamental notions of submodules, factor modules and

Charlatan

遭受

https://doi.org/10.1057/9781137343215mple modules. In this chapter we study modules which are direct sums of simple modules, this leads to the theory of semisimple modules. For some algebras, every module is a direct sum of simple modules. These algebras are said to be semisimple, and they have important applications. In this chapter,

Communicate

Civil Society and Democratic Consolidation, matrix algebras are semisimple algebras. When the coefficient field is algebraically closed the Artin-Wedderburn theorem shows that every semisimple algebra is isomorphic to such an algebra. In general, a semisimple algebra is isomorphic to a direct product of matrix algebras but where matrix block

Enervate

https://doi.org/10.1057/9781137277121over a field is semisimple if and only the characteristic of the coefficient field does not divide the order of the group. We prove this theorem, and we discuss connections between the Artin-Wedderburn decomposition of a semisimple group algebra and properties of the group.

腫塊

https://doi.org/10.1057/9781137277121n finite-dimensional modules. In this setting one considers indecomposable modules, that is, modules which cannot be expressed as direct sums of proper submodules. Every finite-dimensional module is a direct sum of indecomposable modules. A direct sum decomposition into indecomposable summands is es