Document Zbl 0478.16024

Bretscher, Otto; Laeser, Christian; Riedtmann, Christine

Selfinjective and simply connected algebras. (English) Zbl 0478.16024

Manuscr. Math. 36, 253-307 (1981).

Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0478.16024

MSC:

16Gxx	Representation theory of associative rings and algebras
16P10	Finite rings and finite-dimensional associative algebras
16D50	Injective modules, self-injective associative rings
16D80	Other classes of modules and ideals in associative algebras
16D70	Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)

Keywords:

basic, connected, representation-finite, finite dimensional algebra; category of indecomposable modules; mesh-category; Auslander-Reiten quiver; Dynkin graph; translation quiver; configuration; selfinjective algebras; section-algebras; Dynkin quiver; square-free tilting modules

Citations:

Zbl 0455.16014

Cite Review PDF

Full Text: DOI EuDML

References:

[1]	AUSLANDER, M. and I. REITEN: Representation Theory of Artin Algebras III. Comm. Algebra3, 239-294 (1976) · Zbl 0331.16027 · doi:10.1080/00927877508822046
[2]	BONGARTZ, K.: Zykellose Algebren sind nicht zügellos. In: Representation Theory II, LNM 832, pp. 97-102. Berlin-Heidelberg-New York: Springer 1980 · Zbl 0457.16020
[3]	BONGARTZ, K.: Tilted algebras. Proc. of the third Int. Conf. on Rep. of Alg., Puebla 1981. LNM Springer (to appear) · Zbl 0478.16025
[4]	BONGARTZ, K. and P. GABRIEL: Covering spaces in representation theory. To appear in Inventiones Math. · Zbl 0482.16026
[5]	BRETSCHER, O.: Selbstinjektive und einfach zusammenhängende Algebren. Dissertation Uni Zürich 1981
[6]	GABRIEL, P.:Finite representation type is open. In: Representations of algebras, LNM 488, pp. 132-155. Berlin-Heidelfaerg-New York: Springer 1974
[7]	GABRIEL, P.: Auslander-Reiten sequences and representation-finite algebras. In: Representation Theory I, LNM 831, pp. 1-71. Berlin-Heidelberg-New York: Springer 1980
[8]	GABRIEL, P. and C. RIEDTMANN: Group representations without groups. Comment. Math. Helv.54, 240-287 (1979) · Zbl 0447.16023 · doi:10.1007/BF02566271
[9]	HAPPEL, D. and C.M. RINGEL: Tilted algebras. To appear in Trans. Amer. Math. Soc.
[10]	HUGHES, D. and J. WASCHBUESCH: Trivial extensions of tilted algebras. Preprint · Zbl 0488.16021
[11]	RIEDTMANN, C.: Algebren,Oarstellungsköcher und zurück. Comment. Math. Helv.55, 199-224 (1980) · Zbl 0444.16018 · doi:10.1007/BF02566682
[12]	RIEDTMANN, C.: Representation-finite self injective algebras of class An. In: Representation Theory II, LNM 832, pp. 449-520. Berlin-Heidelberg-New York: Springer 1980
[13]	RIEDTMANN, C.: Representation-finite algebras of class Dn. In preparation · Zbl 0455.16014
[14]	RINGEL, C.M.: The rational invariants of the tame quivers, Inventiones Math.58, 217-239 (1980) · Zbl 0433.15009 · doi:10.1007/BF01390253
[15]	GABRIEL, P.: The universal cover of a representation-finite algebra. Proc. of the third Int. Conf. on Rep. of Alg., Puebla 1981, LNM Springer (to appear) · Zbl 0481.16008
[16]	HAPPEL, D. and C.M. RINGEL: Construction of tilted algebras. Proc. of the third Int. Conf. on Rep. of Alg. LNM Springer (to appear) · Zbl 0503.16025
[17]	BRUIJN, N.G. de and B.J.M. MORSELT: A note on planar trees. Journal of Combinatorial Theory2, 27-34 (1967) · Zbl 0147.24005 · doi:10.1016/S0021-9800(67)80111-X

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.