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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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
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