On the Addition of Quantum Matrices

Shahn Majid

doi:10.1063/1.530527

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arXiv · hep-th/9308148

On the Addition of Quantum Matrices

Shahn Majid

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Abstract

We introduce an addition law for the usual quantum matrices $A(R)$ by means of a coaddition $\underlineΔ t=t\otimes 1+1\otimes t$. It supplements the usual comultiplication $Δt=t\otimes t$ and together they obey a codistributivity condition. The coaddition does not form a usual Hopf algebra but a braided one. The same remarks apply for rectangular $m\times n$ quantum matrices. As an application, we construct left-invariant vector fields on $A(R)$ and other quantum spaces. They close in the form of a braided Lie algebra. As another application, the wave-functions in the lattice approximation of Kac-Moody algebras and other lattice fields can be added and functionally differentiated.

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Shahn Majid. 1993-08-30. On the Addition of Quantum Matrices. https://doi.org/10.1063/1.530527

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