Quantum Hyperdeterminants and Hyper-Pfaffians
arXiv:1412.3612 · doi:10.1007/s00209-017-1850-y
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 $q$-analog of Cayley's first hyperdeterminant.
21 pages, updated version, sect. 5 rewritten