The injective tensor product of normal representable bimodules over von Neumann algebras is shown to be normal. The usual Banach module projective tensor product of central representable bimodules over an Abelian C∗-algebra is shown to be representable. A normal version of the projective tensor product is introduced for central normal bimodules.

We use the anomaly cancellation of the M-theory fivebrane to derive the R-symmetry anomalies of the AN (0, 2) tensor-multiplet theories. This result leads to a simple derivation of black hole entropy in d = 4,N = 2 compactifications of M -theory. We also show how the formalism of normal bundle anomaly cancellation clarifies the Kaluza-Klein origin of Chern-Simons terms in gauged supergravity th...

A finite word w is an abelian square if w = xx′ with x′ a permutation of x. In 1972, Entringer, Jackson, and Schatz proved that every binary word of length k2+6k contains an abelian square of length ≥ 2k. We use Cartesian lattice paths to characterize abelian squares in binary sequences, and construct a binary word of length q(q + 1) avoiding abelian squares of length ≥ 2 √ 2q(q + 1) or greater...

Kadanoff’s “correlations along a line” in the critical two-dimensional Ising model [1] are reconsidered. They are the analytical aspect of a representation of abelian chiral vertex operators as quadratic polynomials, in the sense of operator valued distributions, in non-abelian exchange fields. This basic result has interesting applications to conformal coset models. It also gives a new explana...

A partial difference set having parameters (n2, r(n− 1), n+ r2 − 3r, r2 − r) is called a Latin square type partial difference set, while a partial difference set having parameters (n2, r(n+1),−n+r2+3r, r2+r) is called a negative Latin square type partial difference set. Nearly all known constructions of negative Latin square partial difference sets are in elementary abelian groups. In this pape...

The complete geometry of quantum states in parameter space is characterized by the geometric tensor, which contains metric and Berry curvature as real imaginary parts, respectively. When are degenerate, take non-Abelian forms. (Abelian) Abelian have been experimentally measured. However, an feasible scheme to extract all components tensor still lacking. Here we propose a generic protocol direct...

To the memory of Paul Erdd os and to his living heritage Abstract. An abelian square in a binary word is a pair of adjacent non-empty blocks of the same length, having the same number of 1s. An abelian circular square is an abelian square which is possibly wrapped around the word: the tail protruding from the right end of the word reappears at the left end. Two abelian circular squares are equi...

In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders. We define a well-behaved derived Hom-complex with values in the derived category of Hausdorff topological abelian groups. Furthermore we introduce a smallness condition for LCA groups and show that such groups have a...

Erd˝ os introduced the notion of abelian square in a 1961 paper [1]: Definition 1. A word w is an abelian square if there exist two words s and t such that w = st and t is a permutation of s. Maxime Crochemore asked if the language of non-abelian squares is context-free. In this note, we answer his question. Let Σ = {0, 1} be the alphabet in this context. Let L denote the language of all words ...