Foundation of the representation theory of Artin algebras, using the Gabriel-Roiter measure

Ringel CM (2006)
In: Trends in representation theory of algebras and related topics. Workshop on representations of algebras and related topics, Querétaro, México, August 11-14, 2004. Peña JA de la, Bautista R (Eds); Contemporary mathematics, 406. Providence, RI: American Mathematical Society (AMS): 105-135.

Konferenzbeitrag | Veröffentlicht | Englisch
 
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Herausgeber*in
Peña, José Antonio de la; Bautista, Raymundo
Abstract / Bemerkung
These notes are devoted to a single invariant, the Gabriel-Roiter measure of finite length modules: this invariant was introduced by Gabriel (under the name ‘Roiter measure’) in 1972 in order to give a combinatorial interpretation of the induction scheme used by Roiter in his 1968 proof of the first Brauer-Thrall conjecture. It is strange that this invariant (and Roiter’sproof itself) was forgotten in the meantime. One explanation may be that both Roiter and Gabriel pretend that their considerations are restricted to algebras of bounded representation type which are shown to be of finite representation type, thus restricted to algebras of finite representation type. But, as we are going to show, this invariant is of special interest when dealing with algebras of infinite representation type! And there may be a second explanation: in the early seventies, it was possible to calculate this invariant only for few examples, whereas nowadays there is a wealth of methods available. Looking at such examples, we are convinced that the Gabriel-Roiter measure has to be considered as a very important invariant and that it can be used to lay the foundation of the representation theory of artin algebras.
Erscheinungsjahr
2006
Titel des Konferenzbandes
Trends in representation theory of algebras and related topics. Workshop on representations of algebras and related topics, Querétaro, México, August 11-14, 2004
Band
406
Seite(n)
105-135
Konferenz
Workshop on representations of algebras and related topics
Konferenzort
Querétaro, México
Konferenzdatum
2004-08-11 – 2004-08-14
ISBN
978-0-8218-3818-1
Page URI
https://pub.uni-bielefeld.de/record/2940876

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Ringel CM. Foundation of the representation theory of Artin algebras, using the Gabriel-Roiter measure. In: Peña JA de la, Bautista R, eds. Trends in representation theory of algebras and related topics. Workshop on representations of algebras and related topics, Querétaro, México, August 11-14, 2004. Contemporary mathematics. Vol 406. Providence, RI: American Mathematical Society (AMS); 2006: 105-135.
Ringel, C. M. (2006). Foundation of the representation theory of Artin algebras, using the Gabriel-Roiter measure. In J. A. de la Peña & R. Bautista (Eds.), Contemporary mathematics: Vol. 406. Trends in representation theory of algebras and related topics. Workshop on representations of algebras and related topics, Querétaro, México, August 11-14, 2004 (pp. 105-135). Providence, RI: American Mathematical Society (AMS).
Ringel, C. M. (2006). “Foundation of the representation theory of Artin algebras, using the Gabriel-Roiter measure” in Trends in representation theory of algebras and related topics. Workshop on representations of algebras and related topics, Querétaro, México, August 11-14, 2004, Peña, J. A. de la, and Bautista, R. eds. Contemporary mathematics, vol. 406, (Providence, RI: American Mathematical Society (AMS), 105-135.
Ringel, C.M., 2006. Foundation of the representation theory of Artin algebras, using the Gabriel-Roiter measure. In J. A. de la Peña & R. Bautista, eds. Trends in representation theory of algebras and related topics. Workshop on representations of algebras and related topics, Querétaro, México, August 11-14, 2004. Contemporary mathematics. no.406 Providence, RI: American Mathematical Society (AMS), pp. 105-135.
C.M. Ringel, “Foundation of the representation theory of Artin algebras, using the Gabriel-Roiter measure”, Trends in representation theory of algebras and related topics. Workshop on representations of algebras and related topics, Querétaro, México, August 11-14, 2004, J.A. de la Peña and R. Bautista, eds., Contemporary mathematics, vol. 406, Providence, RI: American Mathematical Society (AMS), 2006, pp.105-135.
Ringel, C.M.: Foundation of the representation theory of Artin algebras, using the Gabriel-Roiter measure. In: Peña, J.A. de la and Bautista, R. (eds.) Trends in representation theory of algebras and related topics. Workshop on representations of algebras and related topics, Querétaro, México, August 11-14, 2004. Contemporary mathematics. 406, p. 105-135. American Mathematical Society (AMS), Providence, RI (2006).
Ringel, Claus Michael. “Foundation of the representation theory of Artin algebras, using the Gabriel-Roiter measure”. Trends in representation theory of algebras and related topics. Workshop on representations of algebras and related topics, Querétaro, México, August 11-14, 2004. Ed. José Antonio de la Peña and Raymundo Bautista. Providence, RI: American Mathematical Society (AMS), 2006.Vol. 406. Contemporary mathematics. 105-135.

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