The inhomogeneous quantum invariance group of commuting fermions

Abstract

Abstract:We consider a model of d fermions where creation and annihilation operators of different fermions commute. We show that this particle algebra is invariant under an inhomogeneous quantum group.

The Inhomogeneous Quantum Invariance Group of The Two Parameter Deformed Boson Algebra

“…as a transformation matrix [15][16][17][18][19][20][21] such that it acts on 4 × 1 column vector V by matrix co-multiplication. The elements of the column vector V are the generators of the algebra defined by (9) and (10), namely,…”

The multi-dimensional q-deformed bosonic Newton oscillator and its inhomogeneous quantum invariance group

“…Their hermitian conjugates are denoted by using * notation. Construction of the above transformation matrix will be meaningless unless the non zero elements of matrix M satisfy algebraic relations not only consistent among themselves but also belonging to a Hopf algebra [1][2][3][4][5][11][12][13][14][15][16]. Before writing what these algebraic relations are, let us write the transformed form of the generators of the two dimensional Newton oscillator algebra…”

The inhomogeneous invariance quantum supergroup of supersymmetry algebra

“…However, one can build up a matrix whose elements satisfy Hopf algebra axioms just as the quantum groups which are derived from ordinary groups. [2] In this paper we use the term "invariance quantum supergroup" to describe a…”