We generalize to noncommutative cylinder the solution generation technique, originally suggested for gauge theories on noncommutative plane. For this purpose we construct partial isometry operators and complete set of orthogonal projectors in the algebra A C of the cylinder, and an isomorphism between the free module A C and its direct sum A C ⊕ F C with the Fock module on the cylinder. We cons...

A cosystem consists of a possibly nonselfadoint operator algebra equipped with coaction by discrete group. We introduce the concept C*-envelope for cosystem; roughly speaking, this is smallest C*-algebraic that contains an equivariant completely isometric copy original one. show always exists and we explain how it relates to usual C*-envelope. then compactly aligned product systems over group-e...

We show that if T is an isometry (as metric spaces) between the invertible groups of unital Banach algebras, then T is extended to a surjective real-linear isometry up to translation between the two Banach algebras. Furthermore if the underling algebras are closed unital standard operator algebras, (T (eA)) −1 T is extended to a surjective real algebra isomorphism; if T is a surjective isometry...

Let $G$ be a split connected reductive group over $\mathbb{Z}$. $F$ non-archimedean local field. With $K_m: = Ker(G(\mathfrak{O}_F) \rightarrow G(\mathfrak{O}_F/\mathfrak{p}_F^m))$, Kazhdan proved that for field $F'$sufficiently close to $F$, the Hecke algebras $\mathcal{H}(G(F),K_m)$ and $\mathcal{H}(G(F'),K_m')$ are isomorphic, where $K_m'$ denotes corresponding object $F'$. In this article, ...

For a real reductive dual pair the Capelli identities define a homomorphism C from the center of the universal enveloping algebra of the larger group to the center of the universal enveloping algebra of the smaller group. In terms of the Harish-Chandra isomorphism, this map involves a ρ-shift. We view a dual pair as a Lie supergroup and offer a construction of the homomorphism C based solely on...

The column space of a real n× k matrix x of rank k is a k-plane. Thus we get a map from the space X of such matrices to the Grassmannian G of k-planes in Rn, and hence a GLn-equivariant isomorphism C∞ (G) ≈ C∞ (X)k . We consider the On ×GLk-invariant differential operator C on X given by C = det ( xx ) det ( ∂∂ ) , where x = (xij) , ∂ = ( ∂ ∂xij ) . By the above isomorphism C defines an On-inva...

(abstract) The algebra of all binary relations on a given set is the most important example of a relation algebra (cf. [3]). In this note we will examine the possible isomorphisms within some subclasses of a closely related class (cf. [1] 5.3.2); A is a relation set algebra with base U if its Boolean reduct is a field of sets with unit element 2 U , its universe A contains the identity relation...

for nonnegative integers nβα. Each root β corresponds to a unipotent subgroup Uβ of G, whose Lie algebra is gβ. There is an isomorphism of the additive Lie groupGa ∼= C with Uβ; this is T -equivariant, with multiplication by β(t) on C corresponding to conjugation by t on Uβ (u 7→ tut −1). The product of the groups Uβ for β ∈ R+ forms a unipotent group U , isomorphic to C , with N = #R+, and B =...

The paper presents a construction of the crossed product of a C-algebra by a commutative semigroup of bounded positive linear maps generated by partial isometries. In particular, it generalizes Antonevich, Bakhtin, Lebedev’s crossed product by an endomorphism, and is related to Exel’s interactions. One of the main goals is the Isomorphism Theorem established in the case of actions by endomorphi...