Related papers: Some forms of exceptional Lie algebras
Classical affine Lie algebras appear e.g. as symmetries of infinite dimensional integrable systems and are related to certain differential equations. They are central extensions of current algebras associated to finite-dimensional Lie…
An algebra $L$ over a field $\Bbb F$, in which product is denoted by $[\,,\,]$, is said to be \textit{ Lie type algebra} if for all elements $a,b,c\in L$ there exist $\alpha, \beta\in \Bbb F$ such that $\alpha\neq 0$ and $[[a,b],c]=\alpha…
We classify all integrable complex structures on 6-dimensional Lie algebras of the form $\mathfrak{g}\times\mathfrak{g}$.
Given a non-negative integer $q$, we study two different notions of the $q$-capability of Lie algebras via the non-abelian $q$-exterior product of Lie algebras. The first is related to the $q$-crossed modules and inner $q$-derivations, and…
This article uses Clifford algebra of definite signature to derive octonions and the Lie exceptional algebra G2 from calibrations using Pin(7). This is simpler than the usual exterior algebra derivation and uncovers a subalgebra of Spin(7)…
3-Lie algebras are constructed by Lie algebras, derivations and linear functions, associative commutative algebras, whose involutions and derivations. Then the 3-Lie algebras are obtained from group algebras $F[G]$. An infinite dimensional…
The Z-grading determined by a long simple root of an affine or finite type Lie algebra arises from an adjoint or cominuscule representation of a lower rank semi-simple complex Lie algebra. Analysis of the relationship between the grading…
Exceptional modular invariants for the Lie algebras B2 (at levels 2,3,7,12) and G2 (at levels 3,4) can be obtained from conformal embeddings. We determine the associated alge bras of quantum symmetries and discover or recover, as a…
For sufficiently high dimensions, the naturally graded nonsplit nilpotent Lie algebras with linear characteristic sequence are classified.
Degenerate modules of the exceptional infinite-dimensional simple Lie superalgebras vle(3|6), ksle(5|10) and mb(3|8) have recently been constructed by Kac and Rudakov, and by Grozman, Leites and Shchepochkina. I rederive their results using…
Over an arbitrary field of positive characteristic we construct an example of a locally finite variety of Lie algebras which does not have a finite basis of its polynomial identities. As a consequence we construct varieties of Lie algebras…
We construct, for any integer n greater than or equal to 5, a family of complex filiform Lie algebras with derived length at most 3 and dimension n. We also give examples of n-dimensional filiform Lie algebras with derived length greater…
We study finite dimensional almost and quasi-effective prolongations of nilpotent Z-graded Lie algebras, especially focusing on those having a decomposable reductive structural subalgebra. Our assumptions generalize effectiveness and…
Two new simple modular Lie superalgebras are obtained in characteristics 3 and 5, which share the property that their even parts are orthogonal Lie algebras and the odd parts their spin modules. The characteristic 5 case is shown to be…
We present an extremely elementary construction of the simple Lie algebras over the complex numbers in all of their minuscule representations, using the vertices of various polytopes. The construction itself requires no complicated…
This text gives a construction of a differential graded Lie algebra in Nori's category of effective homological motives. In fact the construction works in more a general setting than that of an Abelian category. This allows us to give the…
We consider modular Lie algebras over algebraically closed field of characteristic $p \geq 7$. This paper purports to prove the conjecture that classical modular Lie algebras,in particular of $C_l$ and of $A_l$ type, should be a Park's Lie…
In this paper we focus on the structure of the variety of Lie algebras with a finite number of ideals and their graph representations using Hasse diagrams. The large number of necessary conditions on the algebraic structure of this type of…
In this paper, we classify solvable quadratic Lie algebras up to dimension 6. In dimensions smaller than 6, we use the Witt decomposition given in \cite{Bou59} and a result in \cite{PU07} to obtain two non-Abelian indecomposable solvable…
There are three kinds of Lie superalgebras for each differentiable manifold. In this note, we shall show an application of the homology groups of those superalgebras in order to classify 4 dimensional Engel-like Lie algebras.