Let A and B be unital semisimple commutative Banach algebras and T a map from the invertible group A onto B. Linearity and multiplicativity of the map are not assumed. We consider the hypotheses on T : (1) σ(TfTg) = σ(fg); (2) σπ(TfTg−α)∩σπ(fg−α) 6= ∅; (3) r(TfTg−α) = r(fg−α) hold for some non-zero complex number α and for every f, g ∈ A, where σ(·) (resp. σπ(·)) denotes the (resp. peripheral) ...

In this paper, we present an expository treatment of the Satake transform. This gives an isomorphism between the spherical Hecke algebra of a split reductive group G over a local field and the representation ring of the dual group Ĝ. If one wants to use the Satake isomorphism to convert information on eigenvalues for the Hecke algebra to local L-functions, it has to be made quite explicit. This...

Let Θ be a variety of algebras, (H, Ψ, f) be a model, where H is an algebra from Θ, Ψ is a set of relation symbols ϕ, f is an interpretation of all ϕ in H. Let X 0 be an infinite set of variables, Γ be a collection of all finite subsets in X 0 (collection of sorts), Φ be the multi-sorted algebra of formulas. These data define a knowledge base KB(H, Ψ, f). In the paper the notion of isomorphism ...

Computably enumerable algebras are the ones whose positive atomic diagrams are computably enumerable. Computable algebras are the ones whose atomic diagrams are computable. In this paper we investigate computably enumerable algebras and provide several algebraic and computable theoretic distinctions of these algebras from the class of computable algebras. We give a characterization of computabl...

We show that the operation of taking generic extensions provides the set of isomorphism classes of representations of a quiver of Dynkin type with a monoid structure. Its monoid ring is isomorphic to the specialization at q = 0 of Ringel’s Hall algebra. This provides the latter algebra with a multiplicatively closed basis. Using a crystal-type basis for a two-parameter quantum group, this multi...

We introduce a nonlocal game that captures and extends the notion of graph isomorphism. This game can be won in the classical case if and only if the two input graphs are isomorphic. Thus, by considering quantum strategies we are able to define the notion of quantum isomorphism. We also consider the case of more general non-signalling strategies, and show that such a strategy exists if and only...

We describe geometric non-commutative formal groups in terms of a geometric commutative formal group with a Poisson structure on its splay algebra. We describe certain natural properties of such Poisson structures and show that any such Poisson structure gives rise to a non-commutative formal group. We describe geometric non-commutative formal groups in terms of a geometric commutative formal g...

We give a geometric description of the fusion rules of the affine Lie algebra ŝu(2)k at a positive integer level k in terms of the k-th power of the basic gerbe over the Lie group SU(2). The gerbe can be trivialised over conjugacy classes corresponding to dominant weights of ŝu(2)k via a 1-isomorphism. The fusion-rule coefficients are related to the existence of a 2-isomorphism between pullback...

Abstract We consider the action of a semisimple Hopf algebra H on an m -Koszul Artin–Schelter regular A . Such is derivation-quotient for some twisted superpotential w , and we show that homological determinant can be easily calculated using Using this, smash product # also algebra, use this to explicitly determine quiver Λ which Morita equivalent, generalising result Bocklandt–Schedler–Wemyss....