It was shown in papers of Dosi and a recent article the author that there is sheaf Frechet-Arens-Michael algebras (locally solvable complex case polynomial growth real) on character space nilpotent Lie algebra. For algebra group affine transformations line (the simplest non-nilpotent algebra) we construct analogous sheaves non-commutative smooth holomorphic functions special set representations.

The Arens-Michael functor in noncommutative geometry is an analogue of the analytification algebraic geometry: out ring “algebraic functions” on a affine scheme, it constructs “holomorphic when viewed as complex analytic space. In this paper, we explicitly compute envelopes Jordan plane and quantum enveloping algebra $U\_q(\mathfrak{sl}(2))$ $\mathfrak{sl}(2)$ for $|q|=1$.

A locally compact group G is discrete if and only the Fourier algebra A(G) has a non-zero (weakly) multiplier. We partially extend this result to setting of ultraspherical hypergroups. Let H be an hypergroup let A(H) denote corresponding algebra. will give several characterizations discreteness in terms algebraic properties A(H). also study Arens regularity closed ideals

1. R. F. Arens, A topology for spaces of transformations, Ann. of Math. vol. 47 (1946) pp. 480-495. 2. R. F. Arens ond J. L. Kelley, Characterizations of the space of continuous functions over a compact Hausdorff space, To be published in Trans. Amer. Math. Soc. 3. S. Banach, Théorie des opérations linéaires, Warsaw, 1932. 4. G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloquium Publications...