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Primitively generated Hall algebras
- Source :
- Berenstein, A; & Greenstein, J. (2016). Primitively generated Hall algebras. Pacific Journal of Mathematics, 281(2), 287-331. doi: 10.2140/pjm.2016.281.287. UC Riverside: Retrieved from: http://www.escholarship.org/uc/item/5v39g941, Pacific Journal of Mathematics, vol 281, iss 2
- Publication Year :
- 2016
- Publisher :
- Mathematical Sciences Publishers, 2016.
-
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.<br />Comment: 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)
- Subjects :
- Large class
Pure mathematics
General Mathematics
01 natural sciences
Nichols algebra
Mathematics::Category Theory
Mathematics - Quantum Algebra
0103 physical sciences
FOS: Mathematics
Quantum Algebra (math.QA)
Finitary
Representation Theory (math.RT)
0101 mathematics
Quantum
exact category
Mathematics
Conjecture
PBW property
010102 general mathematics
Condensed Matter::Mesoscopic Systems and Quantum Hall Effect
16. Peace & justice
Pure Mathematics
Hall algebra
010307 mathematical physics
Indecomposable module
Mathematics - Representation Theory
Subjects
Details
- ISSN :
- 00308730
- Volume :
- 281
- Database :
- OpenAIRE
- Journal :
- Pacific Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....d97360f48d4543a06ccd4b90530a1600