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Representations of algebras = tame a...

Pena, Jose Antonio de la.

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Representations of algebras = tame and wild behavior /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Representations of algebras/ by Jose-Antonio de la Pena.
其他題名:	tame and wild behavior /
作者:	Pena, Jose Antonio de la.
出版者:	Cham :Springer International Publishing : : 2022.,
面頁冊數:	xiv, 233 p. :ill., digital ;24 cm.
內容註:	1 Introduction and First Examples -- 2 A Categorical Approach -- 3 Constructive Methods -- 4 Spectral Methods in Representation Theory -- 5 Group Actions on Algebras and Module Categories -- 6 Reflections and Weyl Groups -- 7 Simply Connected Algebras -- 8 Degenerations of Algebras -- 9 Further Comments.
Contained By:	Springer Nature eBook
標題:	Representations of groups. -
電子資源:	https://doi.org/10.1007/978-3-031-12288-0
ISBN:	9783031122880

Representations of algebras = tame and wild behavior /
Pena, Jose Antonio de la.

Representations of algebrastame and wild behavior /[electronic resource] :by Jose-Antonio de la Pena. - Cham :Springer International Publishing :2022. - xiv, 233 p. :ill., digital ;24 cm. - Algebra and applications,v. 302192-2950 ;. - Algebra and applications ;v. 30..

1 Introduction and First Examples -- 2 A Categorical Approach -- 3 Constructive Methods -- 4 Spectral Methods in Representation Theory -- 5 Group Actions on Algebras and Module Categories -- 6 Reflections and Weyl Groups -- 7 Simply Connected Algebras -- 8 Degenerations of Algebras -- 9 Further Comments.

This book offers an original introduction to the representation theory of algebras, suitable for beginning researchers in algebra. It includes many results and techniques not usually covered in introductory books, some of which appear here for the first time in book form. The exposition employs methods from linear algebra (spectral methods and quadratic forms), as well as categorical and homological methods (module categories, Galois coverings, Hochschild cohomology) to present classical aspects of ring theory under new light. This includes topics such as rings with several objects, the Harada-Sai lemma, chain conditions, and Auslander-Reiten theory. Noteworthy and significant results covered in the book include the Brauer-Thrall conjectures, Drozd's theorem, and criteria to distinguish tame from wild algebras. This text may serve as the basis for a second graduate course in algebra or as an introduction to research in the field of representation theory of algebras. The originality of the exposition and the wealth of topics covered also make it a valuable resource for more established researchers.

ISBN: 9783031122880

Standard No.: 10.1007/978-3-031-12288-0doiSubjects--Topical Terms:

519598
Representations of groups.

LC Class. No.: QA176 / .P4 2022

Dewey Class. No.: 512.22

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505 0 $a 1 Introduction and First Examples -- 2 A Categorical Approach -- 3 Constructive Methods -- 4 Spectral Methods in Representation Theory -- 5 Group Actions on Algebras and Module Categories -- 6 Reflections and Weyl Groups -- 7 Simply Connected Algebras -- 8 Degenerations of Algebras -- 9 Further Comments.
520 $a This book offers an original introduction to the representation theory of algebras, suitable for beginning researchers in algebra. It includes many results and techniques not usually covered in introductory books, some of which appear here for the first time in book form. The exposition employs methods from linear algebra (spectral methods and quadratic forms), as well as categorical and homological methods (module categories, Galois coverings, Hochschild cohomology) to present classical aspects of ring theory under new light. This includes topics such as rings with several objects, the Harada-Sai lemma, chain conditions, and Auslander-Reiten theory. Noteworthy and significant results covered in the book include the Brauer-Thrall conjectures, Drozd's theorem, and criteria to distinguish tame from wild algebras. This text may serve as the basis for a second graduate course in algebra or as an introduction to research in the field of representation theory of algebras. The originality of the exposition and the wealth of topics covered also make it a valuable resource for more established researchers.
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