A remark on $C^\ast$-algebras

A Remark on the Deformation of GNS Representations of ∗ - Algebras

Motivated by deformation quantization we investigate the algebraic GNS construction of ∗representations of deformed ∗-algebras over ordered rings and compute their classical limit. The question if a GNS representation can be deformed leads to the deformation of positive linear functionals. Various physical examples from deformation quantization like the Bargmann-Fock and the Schrödinger represe...

A Remark on Simplicity of Vertex Algebras and Lie Conformal Algebras

I give a short proof of the following algebraic statement: if V is a simple vertex algebra, then the underlying Lie conformal algebra is either abelian, or it is an irreducible central extension of a simple Lie conformal algebra. This provides many examples of non-finite simple Lie conformal algebras, and should prove useful for classification purposes.

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

A Remark on Rational Cherednik Algebras and Differential Operators on the Cyclic Quiver

We show that the spherical subalgebra Uk,c of the rational Cherednik algebra associated to Sn ≀ Cl, the wreath product of the symmetric group and the cyclic group of order l, is isomorphic to a quotient of the ring of invariant differential operators on a space of representations of the cyclic quiver of size l. This confirms a version of [EG, Conjecture 11.22] in the case of cyclic groups. The ...

A Remark on the structure of symmetric quantum dynamical semigroups on von Neumann algebras

We study the structure of the generator of a symmetric, conservative quantum dynamical semigroup with norm-bounded generator on a von Neumann algebra equipped with a faithful semifinite trace. For von Neumann algebras with abelian commutant (i.e. type I von Neumann algebras), we give a necessary and sufficient algebraic condition for the generator of such a semigroup to be written as a sum of s...