### The representation type of the full transformation semigroup $T_4$

Ringel CM (2000)
Semigroup Forum 61(3): 429-434.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Einrichtung
Abstract / Bemerkung
Let T-n be the semigroup of all transformations of a set of n elements and k a field of characteristic 0. According to Ponizovskii, the semigroup algebra kT(n) is of finite representation type if n less than or equal to 3, According to Putcha, kT(n) is of infinite representation type if n greater than or equal to 5. Here, we deal with the remaining case n = 4 and show that kT(4) is also of finite representation type. Note that the quiver of kT(4) already has been exhibited by Putcha, here we determine the relations. It turns out that kT(4) is a string algebra and its global dimension is 3.
Erscheinungsjahr
2000
Zeitschriftentitel
Semigroup Forum
Band
61
Ausgabe
3
Seite(n)
429-434
ISSN
0037-1912
Page URI
https://pub.uni-bielefeld.de/record/1619154

### Zitieren

Ringel CM. The representation type of the full transformation semigroup $T_4$. Semigroup Forum. 2000;61(3):429-434.
Ringel, C. M. (2000). The representation type of the full transformation semigroup $T_4$. Semigroup Forum, 61(3), 429-434. doi:10.1007/PL00006040
Ringel, C. M. (2000). The representation type of the full transformation semigroup $T_4$. Semigroup Forum 61, 429-434.
Ringel, C.M., 2000. The representation type of the full transformation semigroup $T_4$. Semigroup Forum, 61(3), p 429-434.
C.M. Ringel, “The representation type of the full transformation semigroup $T_4$”, Semigroup Forum, vol. 61, 2000, pp. 429-434.
Ringel, C.M.: The representation type of the full transformation semigroup $T_4$. Semigroup Forum. 61, 429-434 (2000).
Ringel, Claus Michael. “The representation type of the full transformation semigroup $T_4$”. Semigroup Forum 61.3 (2000): 429-434.

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