Let K be a field. f∈K[[x1,...,xr]] and g∈K[[y1,...,ys]] nonzero elements. If X (resp. Y) is matrix factorization of f g), Yoshino had constructed tensor product (of factorizations) ⊗ˆ such that X⊗ˆY f+g∈K[[x1,...,xr,y1,...,ys]]. In this paper, we propose bifunctorial operation ⊗˜ its variant ⊗˜′ X⊗˜Y X⊗˜′Y are two different factorizations fg∈K[[x1,...,xr,y1,...,ys]]. We call the multiplicative ...

In this article, we show that concerning the spatial tensor product of W∗-algebras, two weak hyperrigid operator systems is hyperrigid. We prove result by demonstrating unital completely positive maps have unique extension property for if and only has systems. Consequently, as a corollary boundary representations representation The an analogue Hopenwasser’s [9] in setting W∗-algebras.

The tensor product $$R\otimes S$$ of two algebras can have its multiplication deformed by a bicharacter to yield twisted ^t . We completely describe the Hochschild cohomology in terms components R and S, including full Gerstenhaber algebra structure. This description generalizes result Bergh Oppermann. A number interesting classes noncommutative arise as products, sometimes non-obvious ways. ma...