By Mahowald M., Priddy S. (eds.)

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The algebra is of dimension four, the center is of dimension one and Der(M2) is of dimension three with basis consisting of three derivations ea = &&aa: eaf = [aa,f}. 5) We notice that the Leibniz rule is here the Jacobi identity. We see also that the left multiplication aaeb of the derivation e\, by the generator aa no longer satisfies the Jacobi identity: it is not a derivation. The vector space Der(M2) is not a left M2 module. This property is generic. If X is a derivation of an algebra A and h an element of A, then hX is not necessarily a derivation: hX(fg) = h(Xf)g + hfXg ?

Y denotes the Euclidean dot product on V = Rd . The pair (A^,-kg) then turns out to be a pre-C*-algebra for a suitable choice of involution and norm. Its C*-completion is denoted by A$. Note that for 6 = 0, the RHS of Formula (15) reduces to the usual commutative product of functions ab. Also, the first order expansion term in 6 of the oscillatory integral (15) is ^ { o , b}. The product a*$b is thus an associative deformation of ab in the direction of the Poisson bracket coming from the action r.

The algebra is of dimension four, the center is of dimension one and Der(M2) is of dimension three with basis consisting of three derivations ea = &&aa: eaf = [aa,f}. 5) We notice that the Leibniz rule is here the Jacobi identity. We see also that the left multiplication aaeb of the derivation e\, by the generator aa no longer satisfies the Jacobi identity: it is not a derivation. The vector space Der(M2) is not a left M2 module. This property is generic. If X is a derivation of an algebra A and h an element of A, then hX is not necessarily a derivation: hX(fg) = h(Xf)g + hfXg ?

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