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A ℤ 4 3 -grading on a 56 -dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type E

Diego Aranda-Orna, Alberto Elduque, Mikhail Kochetov (2014)

Commentationes Mathematicae Universitatis Carolinae

We describe two constructions of a certain ℤ 4 3 -grading on the so-called Brown algebra (a simple structurable algebra of dimension 56 and skew-dimension 1 ) over an algebraically closed field of characteristic different from 2 . The Weyl group of this grading is computed. We also show how this grading gives rise to several interesting fine gradings on exceptional simple Lie algebras of types E 6 , E 7 and E 8 .

A class of fermionic Novikov superalgebras which is a class of Novikov superalgebras

Huibin Chen, Shaoqiang Deng (2018)

Czechoslovak Mathematical Journal

We construct a special class of fermionic Novikov superalgebras from linear functions. We show that they are Novikov superalgebras. Then we give a complete classification of them, among which there are some non-associative examples. This method leads to several new examples which have not been described in the literature.

A new approach to Hom-left-symmetric bialgebras

Qinxiu Sun, Qiong Lou, Hongliang Li (2021)

Czechoslovak Mathematical Journal

The main purpose of this paper is to consider a new definition of Hom-left-symmetric bialgebra. The coboundary Hom-left-symmetric bialgebra is also studied. In particular, we give a necessary and sufficient condition that s -matrix is a solution of the Hom- S -equation by a cocycle condition.

A review on δ-structurable algebras

Noriaki Kamiya, Daniel Mondoc, Susumu Okubo (2011)

Banach Center Publications

In this paper we give a review on δ-structurable algebras. A connection between Malcev algebras and a generalization of δ-structurable algebras is also given.

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