Nakayama algebras and graded trees
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- by B. Rohnes and S. O. Smalø PDF
- Trans. Amer. Math. Soc. 279 (1983), 249-256 Request permission
Abstract:
Let $k$ be an algebraically closed field. We show that if $T$ is a finite tree, then there is a grading $g$ on $T$ such that $(T,g)$ is a representation finite graded tree, and such that the corresponding simply connected $k$-algebra is a Nakayama algebra (i.e. generalized uniserial algebra).References
- Maurice Auslander and Idun Reiten, Representation theory of Artin algebras. IV. Invariants given by almost split sequences, Comm. Algebra 5 (1977), no. 5, 443–518. MR 439881, DOI 10.1080/00927877708822180
- K. Bongartz and P. Gabriel, Covering spaces in representation-theory, Invent. Math. 65 (1981/82), no. 3, 331–378. MR 643558, DOI 10.1007/BF01396624
- P. Gabriel, The universal cover of a representation-finite algebra, Representations of algebras (Puebla, 1980) Lecture Notes in Math., vol. 903, Springer, Berlin-New York, 1981, pp. 68–105. MR 654725
- Herbert Kupisch, Beiträge zur Theorie nichthalbeinfacher Ringe mit Minimalbedingung, J. Reine Angew. Math. 201 (1959), 100–112 (German). MR 104707, DOI 10.1515/crll.1959.201.100
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 279 (1983), 249-256
- MSC: Primary 16A64; Secondary 16A46
- DOI: https://doi.org/10.1090/S0002-9947-1983-0704614-5
- MathSciNet review: 704614