We prove that an associative algebra A is isomorphic to a subalgebra of a C∗-algebra if and only if its ∗-double A∗A∗ is ∗-isomorphic to a ∗-subalgebra of a C∗-algebra. In particular each operator algebra is shown to be completely boundedly isomorphic to an operator algebra B with the greatest C∗-subalgebra consisting of the multiples of the unit and such that each element in B is determined by...

The following integrability theorem for vertex operator algebras V satisfying some finiteness conditions (C2-cofinite and CFT-type) is proved: the vertex operator subalgebra generated by a simple Lie subalgebra g of the weight one subspace V1 is isomorphic to the irreducible highest weight ĝ-module L(k, 0) for a positive integer k, and V is an integrable ĝ-module. The case in which g is replace...

This paper builds on the previous paper by the author, where a relationship between Zhedanov’s algebra AW (3) and the double affine Hecke algebra (DAHA) corresponding to the Askey-Wilson polynomials was established. It is shown here that the spherical subalgebra of this DAHA is isomorphic to AW (3) with an additional relation that the Casimir operator equals an explicit constant. A similar resu...

Let $\mathfrak{j}$ and $\mathfrak{j}^{'}$ be the Cartan subalgebras of complex semi-simple Lie algebras $\mathfrak{g}$ $\mathfrak{g}^{'}$, $\mathfrak{j}^{*}$ $(\mathfrak{j}^{'})^{*}$ their duals, $\mathfrak{j}^{\vee}$ $(\mathfrak{j}^{'})^{\vee}$ biduals respectively. We consider $B(.,.)$, restriction to Killing form $\mathfrak{g}^{'}$. In this work, using kernel $K$ reproducing subalgebra an op...