Jinsen Zhou | Searcharxiv

arXiv2018

Quadratic Leibniz conformal algebras

In this paper, we study a class of Leibniz conformal algebras called quadratic Leibniz conformal algebras. An equivalent characterization of a Leibniz conformal algebra $R=\mathbb{C}[\partial]V$ through three algebraic operations on $V$ are given. By this characterization, several constructions of quadratic Leibniz conformal algebras are presented. Moreover, one-dimensional central extensions of quadratic Leibniz conformal algebras are considered using some bilinear forms on $V$. In particular, we also study one-dimensional Leibniz central extensions of quadratic Lie conformal algebras.

math.QA↗

arXiv2016

Generalized derivations of n-Hom Lie superalgebras

It is well known that n-Hom Lie superalgebras are certain generalizations of n-Lie algebras. This paper is devoted to investigate the generalized derivations of multiplicative n-Hom Lie superalgebras. We generalize the main results of Leger and Luks to the case of multiplicative n-Hom Lie superalgebras. Firstly, we review some concepts associated with a multiplicative n-Hom Lie superalgebra $N$. Furthermore, we give the definitions of the generalized derivations, quasiderivations, center derivations, centroids and quasicentroids. Obviously, we have the following tower $ZDer(N)\subseteq Der(N)\subseteq QDer(N)\subseteq GDer(N)\subseteq End(N)$. Later on, we give some useful properties and connections between these derivations. Moreover, we obtain that the quasiderivation of $N$ can be embedded as a derivation in a larger multiplicative n-Hom Lie superalgebra. Finally, we conclude that the derivation of the larger multiplicative n-Hom Lie superalgebra has a direct sum decomposition when the center of $N$ is equal to zero.

math.RA↗