Related papers: On Higher {g_n, h_n}-derivations

We study the general Jordan type of standard graded Artinian Gorenstein algebras, it is a finer invariant than Weak and Strong Lefschetz properties for those algebras. We prove that their Jordan types are determined by the rank of certain…

In this paper, we study Jordan derivation-like maps on the $\theta-$Lau products of algebras. We characterize them and prove that under certain condition any Jordan derivation-like maps on the $\theta-$Lau products is a derivation-like map.…

We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of $(\alpha, \beta)$-derivation to $(\alpha, \beta)$-higher derivation and demonstrate that a filter of a hereditary…

Differential categories provide the categorical foundations for the algebraic approaches to differentiation. They have been successful in formalizing various important concepts related to differentiation, such as, in particular,…

In this paper we explore graded algebras of quotients of Lie algebras with special emphasis on the 3-graded case and answer some natural questions concerning its relation to maximal Jordan systems of quotients.

We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie superalgebra were introduced in our earlier…

We present a new aspect of the study of higher derived limits. More precisely, we introduce a complexity measure for the elements of higher derived limits over the directed set $\Omega$ of functions from $\mathbb{N}$ to $\mathbb{N}$ and…

Higher-derivative generalization of the supersymmetric quantum mechanics is proposed. It is formally based on the standard superalgebra but supercharges involve differential operators of the order $n$. As a result, their anticommutator…

In this paper we study irreducible unitary representations of GL(n,R) and prove a number of results. Our first result establishes a precise connection between the annihilator of a representation and the existence of degenerate Whittaker…

Let $T$ be a monad on a category $\mathscr{C}$. In this paper, we introduce the notion of higher derivations on the monad $T$ and characterize them in terms of ordinary derivations on $T$. We also define higher derivations on modules over…

Let $\Gamma$ be a connected graph without loops, cycles or multiple edges and $Z(\Gamma)$ the corresponding zigzag algebra. Then every Jordan derivation of $Z(\Gamma)$ is a derivation. Moreover, we will prove that the dimension of 1th…

In the context of infinity categories, we rethink the notion of derived functor in terms of correspondences. This is especially convenient for the description of a passage from an adjoint pair (F,G) of functors to a derived adjoint pair…

We classify gradings by arbitrary abelian groups on the classical simple Lie and Jordan superalgebras $Q(n)$, $n \geq 2$, over an algebraically closed field of characteristic different from $2$ (and not dividing $n+1$ in the Lie case): fine…

We describe a conjecture on the algebra of higher cohomology operations which leads to the computations of the differentials in the Adams spectral sequence. For this we introduce the notion of an n-th order track category which is suitable…

Higher derivations on an associative algebra generalizes higher order derivatives. We call a tuple consisting of an algebra and a higher derivation on it by an AssHDer pair. We define a cohomology for AssHDer pairs with coefficients in a…

In this paper, bimodules over Hom-Jordan algebras and the ones over Hom-alternative algebras are defined. It is shown that bimodules over Jordan and alternative algebras are twisted into bimodules over Hom-Jordan and Hom-alternative…

The Jordan type of an element $\ell$ of the maximal ideal of an Artinian k-algebra A acting on an A-module M of k-dimension n, is the partition of n given by the Jordan block decomposition of the multiplication map $m_\ell$ on M. In general…

Models of all the gradings on the exceptional simple Lie algebras induced by Jordan subgroups of their groups of automorphisms are provided.

We consider the derivatives of Horn hypergeometric functions of any number variables with respect to their parameters. The derivative of the function in $n$ variables is expressed as a Horn hypergeometric series of $n+1$ infinite summations…

Determining the Jordan canonical form of the tensor product of Jordan blocks has many applications including to the representation theory of algebraic groups, and to tilting modules. Although there are several algorithms for computing this…