Higher Tetrahedral Algebras

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...

Lie-type higher derivations on operator algebras

 Motivated by the intensive and powerful works concerning additive‎ ‎mappings of operator algebras‎, ‎we mainly study Lie-type higher‎ ‎derivations on operator algebras in the current work‎. ‎It is shown‎ ‎that every Lie (triple-)higher derivation on some classical operator‎ ‎algebras is of standard form‎. ‎The definition of Lie $n$-higher‎ ‎derivations on operator algebras and related pot...

Higher Categorified Algebras versus Bounded Homotopy Algebras

We define Lie 3-algebras and prove that these are in 1-to-1 correspondence with the 3-term Lie infinity algebras whose bilinear and trilinear maps vanish in degree (1, 1) and in total degree 1, respectively. Further, we give an answer to a question of [Roy07] pertaining to the use of the nerve and normalization functors in the study of the relationship between categorified algebras and truncate...

Higher order peak algebras

Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras (Sym(N))N≥1, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N = 1 and N = 2). We compute their Hilbert series, introduce and study several combinatorial bases, and establish various algebraic identities related to the multisection...