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...

This article is part of a study on solvable Leibniz algebras with given nilradical. In this paper, algebras, whose nilradical naturally graded quasi-filiform algebra and the complemented space to has maximal dimension, are described up isomorphism.

We give a classification theorem for unital separable nuclear simple C∗-algebras with tracial rank no more than one. Let A and B be two unital separable simple nuclear C∗-algebras with TR(A), TR(B) ≤ 1 which satisfy the universal coefficient theorem. We show that A ∼= B if and only if there is an order and unit preserving isomorphism γ = (γ0, γ1, γ2) : (K0(A),K0(A)+, [1A],K1(A), T (A)) ∼= (K0(B...

This paper provides a survey for the latest developments in the theory of affine q-Schur algebras and Schur–Weyl duality between affine quantum gln and affine type A Hecke algebras. More precisely, we will establish, on the one side, an isomorphism between the double Ringel–Hall algebra D△(n) of a cyclic quiver △(n) and the quantum loop algebra of gln, and establish, on the other side, explicit...

Given a k-graph Λ and an element p of N, we define the dual k-graph, pΛ. We show that when Λ is row-finite and has no sources, the C∗-algebras C∗(Λ) and C∗(pΛ) coincide. We use this isomorphism to apply Robertson and Steger’s results to calculate the K-theory of C∗(Λ) when Λ is finite and strongly connected and satisfies the aperiodicity condition.

We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah-Hirzebruch type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum-Connes and Farrell-Jones to compute alg...

A bstract We investigate two dimensional (2d) quantum field theories which exhibit Non-Lorentzian Kač-Moody (NLKM) algebras as their underlying symmetry. Our investigations encompass both 2d Galilean (speed of light c → ∞) and Carrollian ( 0) CFTs with additional number infinite non-Abelian currents, stemming from an isomorphism between the algebras. alternate intrinsic a limiting analysis. NLK...

The isomorphism problem means to decide if two given finitedimensional simple algebras over the same centre are isomorphic and, if so, to construct an isomorphism between them. A solution to this problem has applications in computational aspects of representation theory, algebraic geometry and Brauer group theory. The paper presents an algorithm for cyclic algebras that reduces the isomorphism ...

Let G be a simple algebraic group of type A or D defined over C and T be a maximal torus of G. For a dominant coweight λ of G, the T -fixed point subscheme (Gr λ G) T of the Schubert variety Gr λ G in the affine Grassmannian GrG is a finite scheme. We prove that there is a natural isomorphism between the dual of the level one affine Demazure module corresponding to λ and the ring of functions (...

We construct an isomorphism of graded Frobenius algebras between the orbifold Chow ring of weighted projective spaces and graded algebras of groups of roots of the unity.