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Generators for K-theoretic Hall algebras of quivers with potential.
- Source :
-
Selecta Mathematica, New Series . Feb2024, Vol. 30 Issue 1, p1-37. 37p. - Publication Year :
- 2024
-
Abstract
- K-theoretic Hall algebras (KHAs) of quivers with potential (Q, W) are a generalization of preprojective KHAs of quivers, which are conjecturally positive parts of the Okounkov–Smironov quantum affine algebras. In particular, preprojective KHAs are expected to satisfy a Poincaré–Birkhoff–Witt theorem. We construct semi-orthogonal decompositions of categorical Hall algebras using techniques developed by Halpern-Leistner, Ballard–Favero–Katzarkov, and Špenko–Van den Bergh. For a quotient of KHA (Q , W) Q , we refine these decompositions and prove a PBW-type theorem for it. The spaces of generators of KHA (Q , 0) Q are given by (a version of) intersection K-theory of coarse moduli spaces of representations of Q. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRA
*K-theory
*GENERALIZATION
Subjects
Details
- Language :
- English
- ISSN :
- 10221824
- Volume :
- 30
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Selecta Mathematica, New Series
- Publication Type :
- Academic Journal
- Accession number :
- 174526937
- Full Text :
- https://doi.org/10.1007/s00029-023-00891-6