THE q-ANALOGUE OF BOSONS AND HALL ALGEBRAS

ABSTRACT

For the q-analogue of boson associated to a hereditary algebra over a finite field k we generalize the result of M. Kashiwara to show that the category of integrable -modules is semisimple, and the positive part of the quantized generalized Kac-Moody algebra associated to represents the unique isoclass of simple objects. Hence we obtain another proof of the result due to B. Sevenhant-M. Van den Bergh that is isomorphic to the twisted Hall algebra .

ACKNOWLEDGMENTS

The author is grateful to Professor Liangang Peng for his help. The author also thanks the referee for his helpful comments on the manuscript. Supported partially by an NSF grant of China and a foundation grant of Ministry of Education of China.