Tame algebras and Tits quadratic forms
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Thu, 27/10/2011 14:00 |
Andrzej Skowronski (Torun) |
Representation Theory Seminar  |
L3 |
| The class of finite dimensional algebras over an algebraically closed field K may be divided into two disjoint subclasses (tame and wild dichotomy). One class consists of the tame algebras for which the indecomposable modules occur, in each dimension d, in a finite number of discrete and a finite number of one-parameter families. The second class is formed by the wild algebras whose representation theory comprises the representation theories of all finite dimensional algebras over K. Hence, the classification of the finite dimensional modules is feasible only for the tame algebras. Frequently, applying deformations and covering techniques, we may reduce the study of modules over tame algebras to that for the corresponding simply connected tame algebras. We shall discuss the problem concerning connection between the tameness of simply connected algebras and the weak nonnegativity of the associated Tits quadratic forms, raised in 1975 by Sheila Brenner. | |||