counterpart , these new observables in A∈A ( ) ′′ A A ω π A have no abstract counterpart in . However, they will have an abstract counterpart in . There is also a natural embedding of A into ∗∗ ∗∗ ∗∗ ⊆ A A A such that . The most common way to construct a von Neumann algebra is to start with a C*-algebra and an abstract state A ω , construct a representation ( , ω ) π ω π H ( via the GNS theorem...

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 ...

Bifunctional mechanism and Pt–Had binding energy can be discriminated by a new descriptor, Q(Hupd) : Q(Coz+) ratio to tailor the HOR activity on Pt–Co surface in alkaline environment.

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...

Abstract. Newman, Schneider and Shalev defined the entropy of a graded associative algebra A as H(A) = lim sup n→∞ n √ an, where an is the vector space dimension of the n’th homogeneous component. When A is the homogeneous quotient of a finitely generated free associative algebra, they showed that H(A) ≤ √ a2. Using some results of Friedland on the maximal spectral radius of (0, 1)-matrices wit...

The present paper addresses the problem of attainment of the supremums in various equivalent definitions of hereditary density hd and hereditary Lindelöf degree hL of Boolean algebras. We partially answer two problems of J. Donald Monk, [13, Problems 50, 54], showing consistency of different attainment behaviour and proving that (for the considered variants) this is the best result we can expec...

Some Lie algebra analogues of Schur's theorem and its converses are presented. As a result, it is shown that for a capable Lie algebra L we always have dim L=Z(L) 2(dim(L2))2. We also give give some examples sup- porting our results.

‎In this paper‎, ‎algebraic investigations on sup-$Sigma$-algebras are presented‎. ‎A representation theorem for‎ ‎sup-$Sigma$-algebras in terms of nuclei and quotients is obtained‎. ‎Consequently‎, ‎the relationship between‎ ‎the congruence lattice of a sup-$Sigma$-algebra and the lattice of its nuclei is fully developed.