Hom-Alternative, Hom-Malcev and Hom-Jordan Superalgebras

Abstract

Hom-alternative, Hom-Malcev and Hom-Jordan superalgebras are Z 2 -graded generalizations of Hom-alternative, Hom-Malcev and Hom-Jordan algebras, which are Hom-type generalizations of alternative, Malcev and Jordan algebras. In this paper we prove that Hom-alternative superalgebras are Hom-Malcevadmissible and are also Hom-Jordan-admissible. Home-type generalizations of some well known identities in alternative superalgebras, including the Z 2 -graded Bruck-Kleinfled function are obtained.

Supercommutator (Hom-)superalgebras of right (Hom-)alternative superalgebras

“…As an immediate consequence, we have the following corollary (see also [AAM,Theorem 6.1] but the proof uses Lemma 6.1 therein).…”

Some characterizations of color Hom-Poisson algebras

“…It follows that when G = Z2 and ε(x, y) = (−1) xy (resp. G = {0} ) in Denition 2.11, we recover the notion of Hom-exible superalgebra [1] (resp. Hom-exible algebra [25]).…”

“…The purpose of this paper is to study color Hom-Poisson algebras which are rst introduced in [5]. For more informations on other color Hom-type algebras, the reader can refer to [1,3,5,20,27].…”

Brackets with (τ,σ)-derivations and (p,q)-deformations of Witt and Virasoro algebras

“…since these expressions are multiple of basis elements, we must have (1) and c n c m p n+m (p ν(n) q ν(m) − p ν(m) q ν(n) ) = c n+m (p n q m − p m q n ).…”