Higher dimensional classicalW-algebras

Higher-dimensional Temperley-Lieb algebras

A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced. MSC-class: 81R50 (primary), 82B20 (secondary).

Higher dimensional classical W - algebras

Classical W -algebras in higher dimensions are constructed. This is achieved by generalizing the classical Gel’fand-Dickey brackets to the commutative limit of the ring of classical pseudodifferential operators in arbitrary dimension. These W -algebras are the Poisson structures associated with a higher dimensional version of the Khokhlov-Zabolotskaya hierarchy (dispersionless KP-hierarchy). Th...

Higher Dimensional Algebras via Colored Props

Starting from any unital colored PROP P, we define a category P(P) of shapes called P-propertopes. Presheaves on P(P) are called P-propertopic sets. For 0 ≤ n ≤ ∞ we define and study n-time categorified P-algebras as P-propertopic sets with some lifting properties. Taking appropriate PROPs P, we obtain higher categorical versions of polycategories, 2-fold monoidal categories, topological quantu...

Prime Higher Derivations on Algebras

Local higher derivations on C*-algebras are higher derivations

Let $mathfrak{A}$ be a Banach algebra. We say that a sequence ${D_n}_{n=0}^infty$ of continuous operators form $mathfrak{A}$ into $mathfrak{A}$ is a textit{local higher derivation} if to each $ainmathfrak{A}$ there corresponds a continuous higher derivation ${d_{a,n}}_{n=0}^infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $mathfrak{A}$ is a $C^*$-algebra t...