To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of CP, where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is related to the coord...

To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of CP , where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is expected to be rela...

Then C∼(X) df = ⊕sC ∼(X) becomes a graded Q-algebra under the intersection product, and we define D∼(X) to be the Q-subalgebra of C∼(X) generated by the divisor classes: D∼(X) = Q[C ∼(X)]. The elements of D∼(X) will be called the Lefschetz classes on X (for the relation ∼). They are the algebraic classes on X expressible as linear combinations of intersections of divisor classes (including the ...

Let A be the category of unital C∗-algebras. A counterexample is given to show that the unitary group functor U : A −→ Grp (and hence the composite of the forgetful functor G : Grp −→ Set with U) although being a faithful right adjoint, fails to be algebraic even in the commutative case. In so doing, a canonical presentation of any unital C∗-algebra as a quotient of a free product of copies (i....

A non-standard quantum deformation of the two-photon algebra h6 is constructed, and its quantum universal R-matrix is given. Representations of this new quantum algebra are studied on the Fock space and translated into Fock–Bargmann realizations that provide a direct formalism for the definition of deformed states of light. Finally, the isomorphism between h6 and the (1+1) Schrödinger algebra i...

We give an exposition of Novodvorskii’s theorem in Banach algebra K-theory, asserting that the Gelfand transform for a commutative induces isomorphism topological K-theory.

in this paper, we generalize some results from hilbert c*-modules to pro-c*-algebra case. we also give a new proof of the known result that l2(a) is ahilbert module over a pro-c*-algebra a.

In this paper, we will show how one is able to construct a lattice on the completion of an algebra and to obtain an isomorphism to its Caratheodory Extension. In addition, it will be shown that the lattice form a σ-algebra and a complete Heyting algebra of countable type.

The Isomorphism Conjectures are translated into the language of homotopical algebra, where they resemble Thomason’s descent theorems.

In this work we present a new definition to the Partial Crossed Product by actions of inverse semigroups in a C-algebra, without using the covariant representations as Sieben did in [5]. Also we present an isomorphism between the partial crossed products by partial actions of a group G and the partial crossed product by actions of S(G), an inverse semigroup associated to G introduced by Exel in...