Primitively generated Hall algebras
Quantum Algebra
2016-02-24 v5 Representation Theory
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.
Cite
@article{arxiv.1209.2770,
title = {Primitively generated Hall algebras},
author = {Arkady Berenstein and Jacob Greenstein},
journal= {arXiv preprint arXiv:1209.2770},
year = {2016}
}
Comments
36 pages, AMSLaTeX+AMSRefs; introduced multiplicity for elements of Grothendieck monoid; they play the role of root multiplicities in Kac-Moody algebras due to a reformulation of Kac conjecture (see Theorem 1.9)