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arXiv · 1209.2770

Primitively generated Hall algebras

Arkady Berenstein·Jacob Greenstein
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Abstract

In the present paper we show that Hall algebras of finitary exact categories behave like quantum groups in the sense that they are generated by indecomposable objects. Moreover, for a large class of such categories, Hall algebras are generated by their primitive elements, with respect to the natural comultiplication, even for non-hereditary categories. Finally, we introduce certain primitively generated subalgebras of Hall algebras and conjecture an analogue of "Lie correspondence" for those finitary categories.

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Arkady Berenstein, Jacob Greenstein. 2012-09-13. Primitively generated Hall algebras. https://doi.org/10.2140/pjm.2016.281.287

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