English

Quantum SUSY operads

Algebraic Geometry 2022-08-25 v1 Mathematical Physics Algebraic Topology math.MP

Abstract

In a recent paper, we described a lifting of coordinate rings of groups, loops, quantum groups, etc. to the categoric setup of operads. In most examples of that paper, these rings are non--commutative. Quantum physics of the XX--th century added one more, quite nontrivial degree of freedom: coordinates might become fermionic. In their classical version, the fermionic coordinates anti--commute, and the resulting rings are called supersymmetric, or SUSY, ones. In this paper, we try to lift operads involving fermionic coordinates to quantum operads. We have to restrict ourselves by lifting operads of supersymmetric rings. We also show that 1D1D supersymmetric algebras have an operad structure, and we analyze their symmetries, through their relation to Adinkra graphs, dessins and codes.

Keywords

Cite

@article{arxiv.2208.11629,
  title  = {Quantum SUSY operads},
  author = {N. C. Combe and Yu. I. Manin and M. Marcolli},
  journal= {arXiv preprint arXiv:2208.11629},
  year   = {2022}
}

Comments

arXiv admin note: text overlap with arXiv:2112.15237

R2 v1 2026-06-25T01:56:29.927Z