in this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a banach algebra $a$ into a semisimple banach algebra $b$ is continuous.

This is the second of three lectures on introduction to vertex operator algebras. In this lecture, we shall continue Professor Dong’s lecture to present more fundamental properties of vertex operator algebras. From the mathematical point of view, a vertex operator algebra formally resembles a Lie algebra because the Jacobi identity is used as one of the main axioms. For the Lie algebra aspect o...

in [1,2,3], a. c. baker and j.w. baker studied the subspace ma(s) of the convolution measure algebra m, (s) of a locally compact semigroup. h. dzinotyiweyi in [5,7] considers an analogous measure space on a large class of c-distinguished topological semigroups containing all completely regular topological semigroups. in this paper, we extend the definitions to study the weighted semigroup algeb...

In this article we review first some of the possibilities in which the notions of Følner sequences and quasidiagonality have been applied to spectral approximation problems. We construct then a canonical Følner sequence for the crossed product of a concrete C∗-algebra and a discrete amenable group. We apply our results to the rotation algebra (which contains interesting operators like almost Ma...

Studying quantum entanglement in systems of indistinguishable particles, particular anyons, poses subtle challenges. Here, we investigate a model one-dimensional anyons defined by generalized algebra. This algebra has the special property that fermions this are composites anyons. A Hubbard-like Hamiltonian is considered allows hopping between nearest neighbor sites not just for fundamental but ...

To any manifold equipped with a higher degree closed form, one can associate an L∞-algebra of local observables that generalizes the Poisson algebra of a symplectic manifold. Here, by means of an explicit homotopy equivalence, we interpret this L∞-algebra in terms of infinitesimal autoequivalences of higher prequantum bundles. By truncating the connection data on the prequantum bundle, we produ...

In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...

We develop results which show that elements in the radical of a commutative Banach algebra are often precluded from having prime-like properties if we avoid certain exceptional situations involving torsion elements. This makes the proof of the Singer-Wermer conjecture conceptually much clearer. It also motivates the de nition of an element having regular powers and allows us to strengthen our p...

In [2], A.Alekseev and E.Meinrenken construct an explicit G-differential space homomorphism Q, called the quantization map, between the Weil algebra Wg = S(g ) ⊗ ∧(g) and Wg = U (g) ⊗ Cl(g) (which they called the noncommutative Weil algebra) for any quadratic Lie algebra g. They showed that Q induces an algebra isomorphism between the basic cohomology rings H bas(Wg) and H ∗ bas(Wg). In this pa...

in this paper we investigate some hereditary properties of amenability modulo an ideal of banach algebras. we show that if (e) is a bounded approximate identity modulo i of a banach algebra a and x is a neo-unital modulo i, then (e) is a bounded approximate identity for x. moreover we show that amenability modulo an ideal of a banach algebra a can be only considered by the neo-unital modulo...