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Journal of the London Mathematical Society Advance Access originally published online on October 16, 2009
Journal of the London Mathematical Society 2009 80(3):771-784; doi:10.1112/jlms/jdp054
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© 2009 London Mathematical Society

The Hall algebra of a spherical object

Bernhard Keller

Institut de Mathématiques de Jussieu
UMR 7586 du CNRS
Université Paris Diderot – Paris 7
UFR de Mathématiques
Case 7012
2 place Jussieu
75251 Paris
Cedex 05
France

Dong Yang

Max-Planck-Institut für Mathematik
Vivatsgasse 7
D-53111 Bonn
Germany
dyang@mpim-bonn.mpg.de

Guodong Zhou

Institut für Mathematik
Universität Paderborn
D-33095 Paderborn
Germany
gzhou@math.uni-paderborn.de

We determine the Hall algebra, in the sense of B. Toën, of the algebraic triangulated category generated by a spherical object.

2000 Mathematics Subject Classification 17B37, 18E30, 16E45.

The second author gratefully acknowledges a postdoctoral fellowship granted by the Université Pierre et Marie Curie, during which this work was carried out. The third author benefited from financial support via postdoctoral fellowships from the Ecole Polytechnique and from the network ‘Representation theory of algebras and algebraic Lie theory’.

Received November 21, 2008; revised June 30, 2009; published online October 16, 2009.


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