Quantum hyperdeterminants and hyper-Pfaffians (Q1686784)

This paper introduces and studies certain quantum analogues of the classical hyperdeterminants and hyper-Pfaffian for hypermatrices. The authors introduce the notion of quantum hypermatrices and constructs a quantum deformation of Cayley's hyperdeterminant for any hypermatrix. It is shown that the quantum hyperdeterminant is a quantum volume element. The notion of quantum hyper-Pfaffian is also introduced and it is shown that it is given by a special volume element of a quantum \(2\)-form.