# On the K-theory of tubular algebras

Colloquium Mathematicae (2000)

- Volume: 86, Issue: 1, page 137-152
- ISSN: 0010-1354

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topKussin, Dirk. "On the K-theory of tubular algebras." Colloquium Mathematicae 86.1 (2000): 137-152. <http://eudml.org/doc/210835>.

@article{Kussin2000,

abstract = {Let Λ be a tubular algebra over an arbitrary base field. We study the Grothendieck group $K_\{0\}(Λ)$, endowed with the Euler form, and its automorphism group $Aut(K_\{0\}(Λ))$ on a purely K-theoretical level as in [7]. Our results serve as tools for classifying the separating tubular families of tubular algebras as in the example [5] and for determining the automorphism group $Aut(D^\{b\}Λ)$ of the derived category of Λ.},

author = {Kussin, Dirk},

journal = {Colloquium Mathematicae},

keywords = {canonical algebras; tubular algebras; Grothendieck groups; Euler forms; separating tubular families; stable tubes; distinction lemma; automorphism groups},

language = {eng},

number = {1},

pages = {137-152},

title = {On the K-theory of tubular algebras},

url = {http://eudml.org/doc/210835},

volume = {86},

year = {2000},

}

TY - JOUR

AU - Kussin, Dirk

TI - On the K-theory of tubular algebras

JO - Colloquium Mathematicae

PY - 2000

VL - 86

IS - 1

SP - 137

EP - 152

AB - Let Λ be a tubular algebra over an arbitrary base field. We study the Grothendieck group $K_{0}(Λ)$, endowed with the Euler form, and its automorphism group $Aut(K_{0}(Λ))$ on a purely K-theoretical level as in [7]. Our results serve as tools for classifying the separating tubular families of tubular algebras as in the example [5] and for determining the automorphism group $Aut(D^{b}Λ)$ of the derived category of Λ.

LA - eng

KW - canonical algebras; tubular algebras; Grothendieck groups; Euler forms; separating tubular families; stable tubes; distinction lemma; automorphism groups

UR - http://eudml.org/doc/210835

ER -

## References

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- [10] H. Lenzing and H. Meltzer, Sheaves on a weighted projective line of genus one, and representations of a tubular algebra, in: Representations of Algebras (Ottawa 1992), V. Dlab and H. Lenzing (eds.), CMS Conf. Proc. 14, Amer. Math. Soc., Providence, RI, 1993, 313-337. Zbl0809.16012
- [11] H. Lenzing and J. A. de la Pe na, Concealed-canonical algebras and separating tubular families, Proc. London Math. Soc. 78 (1999), 513-540. Zbl1035.16009
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