and similarly for the right topological centre Z(r)(A′′). The algebra A is said to be Arens regular if Z(`)(A′′) = Z(r)(A′′) = A′′ and strongly Arens irregular if Z(`)(A′′) = Z(r)(A′′) = A. For example, every C∗-algebra is Arens regular [2]. There has been a great deal of study of these two algebras, especially in the case where A is the group algebra L(G) for a locally compact group G. Results...

We prove that, in the class of commutative topological algebras with separately continuous multiplication, an element is permanently singular if and only if it is a topological divisor of zero. This extends the result given by R. Arens [1] for the Banach algebra case. We also give sufficient conditions for non-removability of ideals in commutative topological algebras with jointly continuous mu...

Let H be a bialgebra and let A be an associative algebra. The algebra A is said to be an H-module-algebra if there is an H-module structure on A such that the multiplication on A becomes an H-module morphism. For example, if S denotes the Landweber-Novikov algebra [15, 21], then the complex cobordism MU(X) of a topological space X is an S module-algebra. Likewise, the singular mod p cohomology ...

Let F denote a totally real number field of degree d > 1 over Q, let p be a prime number and let χ be a totally odd Hecke character of finite order of F . Klingen and Siegel have shown that the values of the Hecke L-series L(χ, s) at integers n ≤ 0 lie in the algebraic closure Q ⊆ C of Q. In [14] Shintani gave another proof by constructing a nice fundamental domain (i.e. a finite disjoint union...

Theorem 2 is also consequence of Theorem 1, so the two theorems are equivalent. In fact, the implication Theorem 1 ⇒ Theorem 2 is usually how one first meets the fundamental theorem of algebra in a linear algebra course: it assures us that any complex square matrix has an eigenvector because the characteristic polynomial of the matrix has a complex root. But here, we will prove Theorem 2 withou...

I discuss tree-level amplitudes in cubic topological string field theory, showing that a certain family of gauge conditions leads to an A∞ algebra of tree-level string products which define a potential describing the dynamics of physical states. Upon using results of modern deformation theory, I show that the string moduli space admits two equivalent descriptions, one given in standard Maurer-C...

‎from hilbert's theorem of zeroes‎, ‎and from noether's ideal theory‎, ‎birkhoff derived certain algebraic concepts (as explained by tholen) that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎i will describe a simple example that illustrates some of the aspects of this relationship‎. the dualization from algebra ...

In the paper, we describe the teleportation from the viewpoints of the braid group and Temperley–Lieb algebra. We propose the virtual braid teleportation which exploits the teleportation swapping and identifies unitary braid representations with universal quantum gates, and further suggest the braid teleportation which is explained in terms of the crossed measurement and the state model of knot...

In this paper, we describe the teleportation from the viewpoints of the braid group and Temperley–Lieb algebra. We propose the virtual braid teleportation which exploits the teleportation swapping and identifies unitary braid representations with universal quantum gates, and suggest the braid teleportation which is explained in terms of the crossed measurement and the state model of knot theory...

For the description of observables and states of a quantum system, it may be convenient to use a canonical Weyl algebra of which only a subalgebra A, with a non-trivial center Z , describes observables, the other Weyl operators playing the role of intertwiners between inequivalent representations ofA. In particular, this gives rise to a gauge symmetry described by the action of Z . A distinguis...