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On the K-theory of tubular algebras

100%

Kussin D.

Colloquium Mathematicum

2000

tom 86

nr 1

137-152

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.

Extremal properties for concealed-canonical algebras

51%

Barot M., Kussin D., Lenzing H.

Colloquium Mathematicum

2013

tom 130

nr 2

183-219

Canonical algebras, introduced by C. M. Ringel in 1984, play an important role in the representation theory of finite-dimensional algebras. They also feature in many other mathematical areas like function theory, 3-manifolds, singularity theory, commutative algebra, algebraic geometry and mathematical physics. We show that canonical algebras are characterized by a number of interesting extremal properties (among concealed-canonical algebras, that is, the endomorphism rings of tilting bundles on a weighted projective line). We also investigate the corresponding class of algebras antipodal to canonical ones. Our study yields new insights into the nature of concealed-canonical algebras, and sheds a new light on an old question: Why are the canonical algebras canonical?

Ograniczanie wyników

2 Colloquium Mathematicum

2 Kussin D.

1 Barot M.

1 Lenzing H.

1 2013

1 2000

Wyniki wyszukiwania

On the K-theory of tubular algebras

Extremal properties for concealed-canonical algebras