Let P be any operad. A P-bimodule R that is a P-cooperad induces a natural “fattening” of the category of P-(co)algebras, expanding the morphism sets while leaving the objects fixed. The morphisms in the resulting R-governed category of P-(co)algebras can be viewed as morphisms “up to R-homotopy” of P-(co)algebras. Let A denote the associative operad in the category of chain complexes. We defin...

Ocneanu noted that the data for what is now known as a Turaev-Viro type TQFT is supplied by a subfactor N of nite index and depth of a II1 factor M . One takes all the irreducible bimodules arising in the decomposition of the tensor powers, in the sense of Connes ([3]), of the Hilbert space L(M) viewed as an N−N bimodule, or, in Connes' terminology, a correspondence. (We will use the term corre...

We study homological and geometric properties of differential algebras of finite type over a base field. The main results concern rigid dualizing complexes over such algebras.

The trellis of a finite Abelian group code is locally (i.e., trellis section by trellis section) related to the trellis of the corresponding dual group code which allows to express the basic operations of the a posteriori probability (APP) decoding algorithm (defined on a single trellis section of the primal trellis) in terms of the corresponding dual trellis section. Using this local approach,...

In [6, Theorem 2.2] Doi gave a Hopf-algebraic proof of a generalization of Oberst’s theorem on affine quotients of affine schemes. He considered a commutative Hopf algebra H over a field, coacting on a commutative H-comodule algebra A. If AcoH denotes the subalgebra of coinvariant elements of A and β : A ⊗AcoH A −→ A ⊗H the canonical map, he proved that the following are equivalent: (a) AcoH ⊂ ...

The interaction between Harmonic Analysis and Operator Theory has been fruitful. In [1] Arveson related results in the Theory of Operator Algebras to such in Spectral Synthesis. He defined synthesis for subspace lattices and proved that certain classes of lattices are synthetic. The main result in this note is a generalization of a result of Arveson for the case of subspace maps. In order to de...