Let F be a field of characteristic 0, and let F be a finite dimensional vector space over F. Let E denote the algebra of all endomorphisms of V, and let L be any Lie subalgebra of E. Among the algebraic Lie algebras contained in E and containing L, there is one that is contained in all of them, and this is called the algebraic hull of L in E. Here, an algebraic Lie algebra is defined as the Lie...

An action of Z by automorphisms of a k-graph induces an action of Z by automorphisms of the corresponding k-graph C∗-algebra. We show how to construct a (k + l)-graph whose C∗-algebra coincides with the crossed product of the original k-graph C∗-algebra by Z. We then investigate the structure of the crossed-product C∗-algebra.

An action of Z by automorphisms of a k-graph induces an action of Z by automorphisms of the corresponding k-graph C∗-algebra. We show how to construct a (k + l)-graph whose C∗-algebra coincides with the crossed product of the original k-graph algebra by Z. We then investigate the structure of the crossed-product C∗-algebra.

In [8], Dirk Kreimer discovered the striking fact that the process of renormalization in quantum field theory may be described, in a conceptual manner, by means of certain Hopf algebras (which depend on the chosen renormalization scheme). A toy model was studied in detail by Alain Connes and Dirk Kreimer in [3]; the Hopf algebra which occurs, denoted by HR, is the polynomial algebra in an infin...

1.1. Probability spaces as von Neumann algebras. The “classical” measure theoretical approach to the study of actions of groups on the probability space is equivalent to a “non-classical” operator algebra approach due to a well known observation of von Neumann, showing that measure preserving isomorphisms between standard probability spaces (X,μ) are in natural correspondence with ∗-algebra iso...

Given a simple atomic relation algebra A and a finite n ≥ 3, we construct effectively an atomic n-dimensional polyadic equality-type algebra P such that for any subsignature L of the signature of P that contains the boolean operations and cylindrifications, the L-reduct of P is completely representable if and only if A is completely representable. If A is finite then so is P. It follows that th...

Abstract In this paper, we show that Leavitt path algebras of weighted graphs and separated are intimately related. We prove any algebra $L(E,\omega )$ a row-finite vertex graph $(E,\omega is $*$ -isomorphic to the lower certain bipartite $(E(\omega ),C(\omega ))$ . For general locally finite $(E, \omega , quotient $L_1(E,\omega an upper another $(E(w)_1,C(w)^1)$ furthermore introduce ${L^{\mat...

A,(T) = [L9(T) ® LQ(T)]IK where K is the kernel of the convolution operator c:Lp(S>LQ(T)->C0(T) by (f®g)(y)(f* g)(y)-4*(r) is the /?-Fourier algebra which was introduced by Figa-Talamanca in [6] where it was shown that ^ ( T ) * isisometrically isomorphic to MP(T), the bounded, translation invariant, linear operators on LP(T), Herz [11] showed that AP(V) is a Banach algebra under pointwise mult...

The concepts of P-compactness, countable P-compactness, the P-Lindelöf property are introduced in L-topological spaces by means of preopen L-sets and their inequalities when L is a complete DeMorgan algebra. These definitions do not rely on the structure of the basis lattice L and no distributivity in L is required. They can also be characterized by means of preclosed L-sets and their inequalit...

it is shown that every  almost linear bijection $h : arightarrow b$ of a unital $c^*$-algebra $a$ onto a unital$c^*$-algebra $b$ is a $c^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in a$, all $y in a$, and all $nin mathbb z$, andthat almost linear continuous bijection $h : a rightarrow b$ of aunital $c^*$-algebra $a$ of real rank zero onto a unital$c^*$-algebra...