K_q-algebras — Draconitic Research

Abstract

We introduce the notion of K_q-algebra, a conjectural axiomatization of the fusion algebra of rotation-equivariant BPS line defects in a 4d cal N=2 Supersymmetric Quantum Field Theory. We also introduce the notion of RG flow of K_q-algebras, a conjectural axiomatization of the action of Seiberg-Witten type RG flows on line defects. These definitions enrich the theory of cluster algebras, K-theoretic Coulomb branch algebras, skein algebras and quantum groups.

Cite

BibTeX RIS

BibTeX

@misc{gaiotto2026kqalgebras,
  title = {{$K_\mathfrakq$-algebras}},
  author = {Davide Gaiotto},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38702},
  eprint = {2609.38702},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38702},
}

RIS

TY  - UNPB
TI  - K_q-algebras
AU  - Davide Gaiotto
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.38702
UR  - https://arxiv.org/abs/2609.38702
AB  - We introduce the notion of K_q-algebra, a conjectural axiomatization of the fusion algebra of rotation-equivariant BPS line defects in a 4d cal N=2 Supersymmetric Quantum Field Theory. We also introduce the notion of RG flow of K_q-algebras, a conjectural axiomatization of the action of Seiberg-Witten type RG flows on line defects. These definitions enrich the theory of cluster algebras, K-theoretic Coulomb branch algebras, skein algebras and quantum groups.
ER  -