Displaying similar documents to “A classification of low dimensional multiplicative Hom-Lie superalgebras”

Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields

Liping Sun, Wende Liu (2017)

Open Mathematics

Similarity:

According to the classification by Kac, there are eight Cartan series and five exceptional Lie superalgebras in infinite-dimensional simple linearly compact Lie superalgebras of vector fields. In this paper, the Hom-Lie superalgebra structures on the five exceptional Lie superalgebras of vector fields are studied. By making use of the ℤ-grading structures and the transitivity, we prove that there is only the trivial Hom-Lie superalgebra structures on exceptional simple Lie superalgebras....

Hom-structures on semi-simple Lie algebras

Wenjuan Xie, Quanqin Jin, Wende Liu (2015)

Open Mathematics

Similarity:

A Hom-structure on a Lie algebra (g,[,]) is a linear map σ W g σ g which satisfies the Hom-Jacobi identity: [σ(x), [y,z]] + [σ(y), [z,x]] + [σ(z),[x,y]] = 0 for all x; y; z ∈ g. A Hom-structure is referred to as multiplicative if it is also a Lie algebra homomorphism. This paper aims to determine explicitly all the Homstructures on the finite-dimensional semi-simple Lie algebras over an algebraically closed field of characteristic zero. As a Hom-structure on a Lie algebra is not necessarily...

Vector form brackets in Lie algebroids

Albert Nijenhuis (1996)

Archivum Mathematicum

Similarity:

A brief exposition of Lie algebroids, followed by a discussion of vector forms and their brackets in this context - and a formula for these brackets in “deformed” Lie algebroids.

Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebras

Johannes Huebschmann (2000)

Banach Center Publications

Similarity:

Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the almost complex structure is integrable. We characterize twilled LR structures in terms of certain associated differential (bi)graded Lie and G(erstenhaber)-algebras; in particular the G-algebra arising from an almost complex structure is a (strict) d(ifferential)...