<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we find conditions under which the bracket defined by a graded derivation on a Lie superalgebra (<italic>g</italic>, [, ]) is skew-supersymmetry and satisfies the super Jacobi identity, so it defines the structure of a Lie superalgebra on <italic>g.</italic></p><p>In the case of the algebra of differential forms on a supermanifold, we study the graded commutator of graded derivations, graded skew-derivations and a graded derivation, with another graded skew-derivation of the superalgebra of differential forms on a supermanifold.</p></abstract>

In this paper, we find conditions under which the bracket defined by a graded derivation on a Lie superalgebra (g, [, ]) is skew-supersymmetry and satisfies the super Jacobi identity, so it defines the structure of a Lie superalgebra on g.In the case of the algebra of differential forms on a supermanifold, we study the graded commutator of graded derivations, graded skew-derivations and a graded derivation, with another graded skew-derivation of the superalgebra of differential forms on a supermanifold.

On graded derivations of superalgebras

Faculty of Mathematical Sciences Department of Pure Mathematics

General Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On graded derivations of superalgebras"}

In this paper, we find conditions under which the bracket defined by a graded derivation on a Lie superalgebra (g, [, ]) is skew-supersymmetry and satisfies...

On graded derivations of superalgebras

Published Online: Jul 31, 2020

Page range: 3 - 10

Received: Jun 24, 2018

Accepted: Apr 22, 2020

DOI: https://doi.org/10.2478/gm-2020-0001

Keywords
graded manifolds, Lie superalgebra, graded derivation, graded skew-derivation

© 2020 Esmaeil Azizpour et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On graded derivations of superalgebras

Published Online: Jul 31, 2020

Page range: 3 - 10

Received: Jun 24, 2018

Accepted: Apr 22, 2020

DOI: https://doi.org/10.2478/gm-2020-0001

Keywordsgraded manifolds, Lie superalgebra, graded derivation, graded skew-derivation

© 2020 Esmaeil Azizpour et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
graded manifolds, Lie superalgebra, graded derivation, graded skew-derivation