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 -analog of Cayley's first hyperdeterminant.
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