## 12 Citations

DEFORMATIONS OF SOME COLOR LIE SUPERALGEBRAS

- Mathematics
- 2012

In this work infinitesimal deformations of the model filiform Z2 × Z2-color Lie superalgebra have been studied. All the filiform Z2 ×Z2-color Lie superalgebras can be obtained by means of…

A Method for Classifying Filiform Lie Superalgebras

- Mathematics
- 2017

Throughout the present work the latest contributions in determining filiform Lie superalgebras are reviewed. Filiform Lie superalgebras constitute itselves a very important type of nilpotent Lie…

Filiform Z2xZ2-color Lie superalgebras

- Mathematics
- 2013

We continue the study of the filiform Z2xZ2-color Lie superalgebras. All of them can be obtained by using infinitesimal deformations, i.e. cocycles. In this work we give the total dimension of such…

About Filiform Lie Algebras of Order 3

- Mathematics
- 2015

The aim of this work is to review recent advances in generalizing filiform Lie (super)algebras into the theory of Lie algebras of order F. Recall that the latter type of algebras constitutes the…

Filiform Lie algebras of order 3

- Mathematics
- 2014

The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of…

Z2 and Klein graded Lie algebras

- Mathematics
- 2012

In this master's thesis, we recall the definitions and basic results for Lie superalgebras. We specify the definition for Klein graded Lie algebras and, motivated by well known results for Lie…

## References

SHOWING 1-10 OF 17 REFERENCES

Generalized Lie algebras

- Mathematics
- 1979

The generalized Lie algebras, which have recently been introduced under the name of color (super) algebras, are investigated. The generalized Poincare–Birkhoff–Witt and Ado theorems hold true. We…

Bosonic Realizations of the Colour Heisenberg Lie Algebra

- Mathematics
- 2006

Abstract We describe realizations of the colour analogue of the Heisenberg Lie algebra by power series in non-commuting indeterminates satisfying Heisenberg’s canonical commutation relations of…

Lie Color and Hom-Lie Algebras of Witt Type and Their Central Extensions

- Mathematics
- 2009

In this article, two classes of Г-graded Witt-type algebras, Lie color and hom-Lie algebras of Witt type, are considered. These algebras can be seen as generalizations of Lie algebras of Witt type.…

A complete description of all the infinitesimal deformations of the Lie superalgebra Ln,m

- Mathematics
- 2010

Graded quasi-lie algebras of witt type

- Mathematics
- 2006

In this article, we introduce a new class of graded algebras called quasi-Lie algebras of Witt type. These algebras can be seen as a generalization of other Witt-type algebras like Lie algebras of…

Representations and Cocycle Twists of Color Lie Algebras

- Mathematics
- 2004

We study relations between finite-dimensional representations of color Lie algebras and their cocycle twists. Main tools are the universal enveloping algebras and their FCR-properties…

Z3-grading and the cubic root of the Dirac equation

- Mathematics
- 1992

A generalisation of supersymmetry is proposed based on Z3-graded algebras. Introducing the objects whose ternary communication relations contain the cubic roots of unity, e2 pi i/3, e4 pi i/3 and 1,…

Hypersymmetry: A Z3-graded generalization of supersymmetry

- Mathematics
- 1997

We propose a generalization of non-commutative geometry and gauge theories based on ternary Z3-graded structures. In the new algebraic structures we define, all products of two entities are left…