Hall algebras revisited

Ringel CM (1992) Preprint / Universität Bielefeld, Sonderforschungsbereich 343, Diskrete Strukturen in der Mathematik ; 92,29.
Bielefeld.

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Abstract
For any finite-dimensional algebra over a finite field, the corresponding Hall algebra has been introduced in order to handle the possible filtrations of modules with fixed factors. For the path algebra of a Dynkin diagram with a fixed orientation, it has been shown that the Hall algebra satisfies relations which are similar to the Drinfeld-Jimbo relations defining quantum groups, but they depend on the chosen orientation. The purpose of this note is to adjust the multiplication of a Hall algebra in order to obtain the Drinfeld-Jimbo relations themselves. The additional factor introduced in our change of multiplication involves the Euler characteristic, in this way we eliminate the dependence on the orientation.
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Ringel CM. Hall algebras revisited. Preprint / Universität Bielefeld, Sonderforschungsbereich 343, Diskrete Strukturen in der Mathematik ; 92,29. Bielefeld; 1992.
Ringel, C. M. (1992). Hall algebras revisited (Preprint / Universität Bielefeld, Sonderforschungsbereich 343, Diskrete Strukturen in der Mathematik ; 92,29). Bielefeld.
Ringel, C. M. (1992). Hall algebras revisited. Preprint / Universität Bielefeld, Sonderforschungsbereich 343, Diskrete Strukturen in der Mathematik ; 92,29, Bielefeld.
Ringel, C.M., 1992. Hall algebras revisited, Preprint / Universität Bielefeld, Sonderforschungsbereich 343, Diskrete Strukturen in der Mathematik ; 92,29, Bielefeld.
C.M. Ringel, Hall algebras revisited, Preprint / Universität Bielefeld, Sonderforschungsbereich 343, Diskrete Strukturen in der Mathematik ; 92,29, Bielefeld: 1992.
Ringel, C.M.: Hall algebras revisited. Preprint / Universität Bielefeld, Sonderforschungsbereich 343, Diskrete Strukturen in der Mathematik ; 92,29. Bielefeld (1992).
Ringel, Claus Michael. Hall algebras revisited. Bielefeld, 1992. Preprint / Universität Bielefeld, Sonderforschungsbereich 343, Diskrete Strukturen in der Mathematik ; 92,29.
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