Let A be a simple separable unital C*-algebra satisfying the UCT, and assume that A has finite decomposition rank. Let Q denote the UHF algebra with K0(Q) = Q. Then A⊗Q can be tracially approximated by unital Elliott-Thomsen algebras, and therefore A ⊗ Z is an ASH algebra (hence classifiable), where Z is the Jiang-Su algebra.

Let $U_{q}'(\mathfrak{g})$ be a quantum affine algebra of untwisted ADE type and let $\mathcal{C}_{\mathfrak{g}}^{0}$ Hernandez-Leclerc’s category. For duality datum $\mathcal{D}$ in $\mathcal{C}_{\mathfrak{g}}^{0}$, we denote by $\mathcal{F}_{\mathcal{D}}$ the Weyl-Schur functor. We give sufficient condition for to provide functor sending simple modules modules. Moreover, under same condition,...

It is well known that the Clifford algebra Cl p,q associated to a nondegenerate quadratic form on R n (n = p + q) is isomorphic to a matrix algebra K(m) or direct sum K(m) ⊕ K(m) of matrix algebras, where K = R, C, H. On the other hand, there are no explicit expressions for these isomorphisms in literature. In this work, we give a method for the explicit construction of these isomorphisms. Let ...

We give the explicite form of the BRST charge Q for the algebra W4 = WA3 in the basis where the spin-3 and the spin-4 field are primary as well as for a basis where the algebra closes quadratically. ∗e-mail: [email protected]; 31890::HORNFECK For the construction of W-strings [1], especially its physical states, it is important to know the cohomology of the BRST charge [2, 3, 4, 5, 6, 7, 8, 9...

In this paper we discuss a relationship between the following two algebras: (i) the subconstituent algebra T of a distance-regular graph that has q-Racah type; (ii) the q-tetrahedron algebra ⊠q which is a q-deformation of the three-point sl2 loop algebra. Assuming that every irreducible T -module is thin, we display an algebra homomorphism from ⊠q into T and show that T is generated by the imag...

Algebra greatly broadened the very notion of algebra in two ways. First, the traditional numerical domains such as Z, Q R, and C, were now seen as instances of more general concepts of equationally-defined algebraic structure, which did not depend on any particular representation for their elements, but only on abstract sets of elements, operations on such elements, and equational properties sa...

We define and study the category Rep(Q, F1) of representations of a quiver in Vect(F1) the category of vector spaces ”over F1”. Rep(Q, F1) is an F1–linear category possessing kernels, co-kernels, and direct sums. Moreover, Rep(Q, F1) satisfies analogues of the Jordan-Hölder and Krull-Schmidt theorems. We are thus able to define the Hall algebra HQ of Rep(Q, F1), which behaves in some ways like ...

EQ-algebras were introduced by Nov?ak in [16] as an algebraic structure of truth values for fuzzy type theory (FTT). Nov?k and De Baets [18] various kinds such good, residuated, lattice ordered EQ-algebras. In any logical structures, using filters, one can construct other structures. With this inspirations, means fantastic filters we MV-algebras. Also, study prelinear introduce a new kind filte...