We study a general Kishimoto’s problem for automorphisms on simple C∗-algebras with tracial rank zero. Let A be a unital separable simple C∗-algebra with tracial rank zero and let α be an automorphism. Under the assumption that α has certain Rokhlin property, we present a proof that A ⋊α Z has tracial rank zero. We also show that if the induced map α∗0 on K0(A) fixes a “dense” subgroup of K0(A)...

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Modulo the ideal generated by the derivative fields, the normal ordered product of holomorphic fields in two-dimensional conformal field theory yields a commutative and associative algebra. The zero mode algebra can be regarded as a deformation of the latter. Alternatively, it can be described as an associative quotient of the algebra given by a modified normal ordered product. We clarify the r...

With each sequence α = (αn)n∈N of pairwise distinct and non-zero points which are such that the canonical product

We determine the number of edges of the zero-divisor graph of the direct product of finitely many finite non-commutative rings or semigoups.

Right groups are direct products of right zero semigroups and groups and they play a significant role in the semilattice decomposition theory of semigroups. Right groups can be characterized as associative right quasigroups (magmas in which left translations are bijective). If we do not assume associativity we get right quasigroups which are not necessarily representable as direct products of r...

We introduce product differentiation in the model of price competition with strictly convex costs in which firms have to supply all the forthcoming demand. We find that although a continuum of equilibria exists in a homogeneous product market, the competitive price equilibrium is the only robust one. Specifically, as long as the equilibrium correspondence is nonempty, the equilibrium price conv...

The problem of efficient implementation of two-dimensional interpolation in the Guruswami-Sudan list decoding algorithm for Reed-Solomon codes is considered. It is shown that it can be implemented by computing the product of the ideals of interpolation polynomials constructed for subsets of interpolation points. A method for fast multiplication of zero-dimensional co-prime ideals product is pro...

We show that if a Blaschke product defines a computable function, then it has a computable sequence of zeros in which the number of times each zero is repeated is its multiplicity. We then show that the converse is not true. We finally show that every computable, radial, interpolating sequence yields a computable Blaschke product.

Consider a tensor product H = H1⊗H2⊗· · ·⊗Hk of finite dimensional Hilbert spaces with dimension of Hi = di, 1 ≤ i ≤ k. Then the maximum dimension possible for a subspace of H with no non-zero product vector is known to be d1d2 . . . dk− (d1 +d2 + · · ·+dk)+k−1. We obtain an explicit example of a subspace of this kind. We determine the set of product vectors in its orthogonal complement and sho...