Based on the Bogoliubov non-ideal gas model, we discuss the energy spectrum and phase transition of the superfluid Fermi gas of atoms with a weak attractive interaction on the canonical noncommutative space. Because the interaction of a BCS-type superfluid Fermi gas originates from a pair of Fermionic quasi-particles with opposite momenta and spins, the Hamiltonian of the Fermi gas on the nonco...

Considering space--time to be non-commutative, we study the evolution of universe employing approach Newtonian cosmology. Generalizing conservation energy and first law thermodynamics $\kappa$-deformed space--time, derive modified Friedmann equations, valid up order, in deformation parameter. Analyzing these deformed time scale factor cases radiation-dominated, matter-dominated, vacuum (energy)...

In 1969 Lindenstrauss and Rosenthal showed that if a Banach space is isomorphic to a complemented subspace of an Lp-space, then it is either a Lp-space or isomorphic to a Hilbert space. This is the motivation of this paper where we study non–Hilbertian complemented operator subspaces of non commutative Lp-spaces and show that this class is much richer than in the commutative case. We investigat...

‎‎Let $R$ be a commutative ring with identity and let $M$ be an $R$-module‎. ‎We define the primary spectrum of $M$‎, ‎denoted by $mathcal{PS}(M)$‎, ‎to be the set of all primary submodules $Q$ of $M$ such that $(operatorname{rad}Q:M)=sqrt{(Q:M)}$‎. ‎In this paper‎, ‎we topologize $mathcal{PS}(M)$ with a topology having the Zariski topology on the prime spectrum $operatorname{Spec}(M)$ as a sub...

Matrix model is used as a regularization of field theory on non-commutative torus. However, there exists an example that the product of the large-N limit of matrices does not coincide with that of the corresponding fields. We propose a new procedure for regularizing fields on a non-commutative torus by matrices with the help of the projection in the representation space, so that the products of...

We compute at the one-loop order the β-functions for a renormalisable noncommutative analog of the Gross Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative field theory exhibits asymptotic freedom for any number of colors. The β-function for the non-commutative counterpart of the Thirring model is found ...

defined by the shuffle of tensors. If the product of A is commutative, then the bar differential is a derivation with respect to the shuffle product so that B(A) is still an associative and commutative differential graded algebra. Unfortunately, in algebraic topology, algebras are usually commutative only up to homotopy: a motivating example is provided by the cochain algebra of a topological s...

Let B be a strictly real commutative real Banach algebra with the carrier space Φ B. If A is a commutative real Banach algebra, then we give a representation of a ring homomorphism ρ : A → B, which needs not be linear nor continuous. If A is a commutative complex Banach algebra, then ρ(A) is contained in the radical of B. 1. Introduction and results. Ring homomorphisms are mappings between two ...

We have discovered an eecient algorithm for matching and uniication in associative-commutative (AC) and associative-commutative-idempotent (ACI) equational theories. In most cases of AC uniication and in all cases of ACI uniication our method obviates the need for solving diophantine equations, and thus avoids one of the bottlenecks of other associative-commutative uniication techniques. The al...

We present here a quite unexpected result: Apart from already known commutative C∗-algebras generated by Toeplitz operators on the unit ball, there are many other Banach algebras generated by Toeplitz operators which are commutative on each weighted Bergman space. These last algebras are non conjugated via biholomorphisms of the unit ball, non of them is a C∗-algebra, and for n = 1 all of them ...