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We establish several properties of a quadratic algebra over a field k, which is a deformation of the symmetric algebra Sk 3 . In particular, we prove that A is an integral domain, noetherian and Koszul; we compute its first Hochschild cohomology group; we determine the corresponding Poisson structure on k 3 and its symplectic leaves; we define an involution on A and describe the corresponding irreducible involutive representations. 1991 Mathematics Subject Classification: 16W10, 18G15.doi:10.4064/ap-66-1-123-135 fatcat:ys7jprz4gfewvgwczcksmc3jfe