Abstract
We show that the deformation of the exterior algebra on a given manifold is related to the existence of the Yang-Baxter equation. We prove that this deformed algebra involves a differential operator generating the algebra. The obtained differential calculus is not commutative and we recover the classical one for the classical limit of the deformation parameters. The q-analogue of the Leibniz rule corresponding to the purposed differential operator is given.
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Daoud, M., Hassouni, Y. & Tahri, E.H. Deformation of the exterior algebra Ω(M n) and the Yang-Baxter equation. Int J Theor Phys 36, 1413–1421 (1997). https://doi.org/10.1007/BF02435935
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DOI: https://doi.org/10.1007/BF02435935