The two-parameter deformation ofGL(2), its differential calculus, and Lie algebra | Zendy

Arne Schirrmacher | Zendy; J. Wess | Zendy; Bruno Zumino | Zendy

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The two-parameter deformation ofGL(2), its differential calculus, and Lie algebra

Author(s) -

Arne Schirrmacher,

J. Wess,

Bruno Zumino

Publication year - 1991

Publication title -

zeitschrift für physik c

Language(s) - English

Resource type - Journals

eISSN - 1431-5858

pISSN - 0170-9739

DOI - 10.1007/bf01555507

Subject(s) - differential calculus , mathematics , lie algebra , invariant (physics) , quantization (signal processing) , algebra over a field , deformation (meteorology) , quantum differential calculus , differential geometry , inverse , pure mathematics , graded lie algebra , mathematical physics , geometry , physics , algorithm , meteorology , noncommutative quantum field theory , noncommutative geometry

The Yang-Baxter equation is solved in two dimensions giving rise to a two-parameter deformation ofGL(2). The transformation properties of quantum planes are briefly discussed. Non-central determinant and inverse are constructed. A right-invariant differential calculus is presented and the role of the different deformation parameters investigated. While the corresponding Lie algebra relations are simply deformed, the comultiplication exhibits both quantization parameters.

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