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Coxeter transformations and the representation theory of algebras

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Finite Dimensional Algebras and Related Topics

Part of the book series: NATO ASI Series ((ASIC,volume 424))

Abstract

This work presents a survey (with some proofs) of the recent developments in the study of Coxeter transformations and their applications to representation theory of associative algebras. Let Q be a quiver and C = C(Q) the associated Coxeter matrix. We consider results on the eigenvalues of C: multiplicities, distribution, bounds, relation with the symmetries of Q... We consider applications to the study of the indecomposable modules over the hereditary algebra k[Q] (k a field): position of modules, growth of the Auslander-Reiten translates... Other applications concern growth of components of the representation-quiver of finite dimensional algebras, towers of algebras...

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Author information

Authors and Affiliations

  1. Instituto de Matemáticas, UNAM, Ciudad Universitaria, México D. F., 04510, Mexico

    José Antonio de la Peña

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  1. José Antonio de la Peña
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Carleton University, K1S 5B6, Ottawa, Ontario, Canada

    Vlastimil Dlab

  2. Department of Mathematics, University of Virginia, 22901, Charlottesville, Virginia, USA

    Leonard L. Scott

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© 1994 Springer Science+Business Media Dordrecht

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de la Peña, J.A. (1994). Coxeter transformations and the representation theory of algebras. In: Dlab, V., Scott, L.L. (eds) Finite Dimensional Algebras and Related Topics. NATO ASI Series, vol 424. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1556-0_12

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  • DOI: https://doi.org/10.1007/978-94-017-1556-0_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4377-1

  • Online ISBN: 978-94-017-1556-0

  • eBook Packages: Springer Book Archive

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