English

Quantum Hyperdeterminants and Hyper-Pfaffians

Quantum Algebra 2017-11-06 v4 Combinatorics Rings and Algebras Representation Theory

Abstract

The notion of generalized quantum monoids is introduced. It is proved that the quantum coordinate ring of the monoid can be lifted to a quantum hyper-algebra, in which the quantum determinant and quantum Pfaffian are sent to the quantum hyperdeterminant and quantum hyper-Pfaffian respectively. The quantum hyperdeterminant in even dimension is shown to be a qq-analog of Cayley's first hyperdeterminant.

Keywords

Cite

@article{arxiv.1412.3612,
  title  = {Quantum Hyperdeterminants and Hyper-Pfaffians},
  author = {Naihuan Jing and Jian Zhang},
  journal= {arXiv preprint arXiv:1412.3612},
  year   = {2017}
}

Comments

21 pages, updated version, sect. 5 rewritten

R2 v1 2026-06-22T07:27:40.902Z