Related papers: On 10 dimensional Exceptional Drinfel'd Algebras
In this paper we give the classification of the irreducible non solvable Lie algebras of dimensions $\leq 13$ with nondegenerate, symmetric and invariant bilinear forms.
We consider N=1 dualities in four dimensional supersymmetric gauge theories as a geometrical realization of wrapping D 6-branes around 3-cycles of Calabi-Yau threefolds in type IIA string theory. By extending the recent work of Ooguri and…
In this note we study exceptional algebroids, focusing on their relation to type IIB superstring theory. We show that a IIB-exact exceptional algebroid (corresponding to the group $E_{n(n)}\times \mathbb{R}^+$, for $n\le 6$) locally has a…
We give a full classification of 6-dimensional nilpotent Lie algebras over an arbitrary field, including fields that are not algebraically closed and fields of characteristic~2. To achieve the classification we use the action of the…
Given a double vector bundle $D\to M$, we define a bigraded `Weil algebra' $\mathcal{W}(D)$, which `realizes' the algebra of smooth functions on the supermanifold $D[1,1]$. We describe in detail the relations between the Weil algebras of…
In this work we study a large class of exact Lie bialgebras arising from noncommutative deformations of Poisson-Lie groups endowed with a left invariant Riemannian metric. We call these structures \emph{exact metaflat Lie bialgebras}. We…
We prove that there are no rigid complex filiform Lie algebras in the variety of (filiform) Lie algebras of dimension less than or equal to 11. More precisely we show that in any Euclidean neighborhood of a filiform Lie bracket (of low…
We determine the isomorphism classes of the first family of infinite dimensional simple Lie algebras recently introduced by Xu. The structure space of these algebras is given explicitly. The derivations of these algebras are also…
In the present paper we review the progress of the project of classification and construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we called earlier…
We equip a family of algebras whose noncommutativity is of Lie type with a derivation based differential calculus obtained, upon suitably using both inner and outer derivations, as a reduction of a redundant calculus over the Moyal four…
We classify irreducible finite-dimensional modules of a collection of real Lie superalgebras that includes the simple ones, their classical variants, complex Lie superalgebras after restriction of scalars, and all real Lie algebras. Our…
We define Drinfeld orbifold algebras as filtered algebras deforming the skew group algebra (semi-direct product) arising from the action of a finite group on a polynomial ring. They simultaneously generalize Weyl algebras, graded (or…
A double extension ($\mathscr{D}$ extension) of a Lie (super)algebra $\mathfrak a$ with a non-degenerate invariant symmetric bilinear form $\mathscr{B}$, briefly: a NIS-(super)algebra, is an enlargement of $\mathfrak a$ by means of a…
We study constraints imposed by four-dimensional unitarity (formalised as graded unitarity in recent work by the first author) on possible ${\mathcal W}_3$ vertex algebras arising from four-dimensions via the SCFT/VOA correspondence. Under…
Recently one of the authors obtained a classification of simple infinite-dimensional Lie superalgebras of vector fields which extends the well-known classification of E. Cartan in the Lie algebra case. The list consists of many series…
In this paper, we give a generalization of results in \cite{PU07} and \cite{DPU10} by applying the tools of graded Lie algebras to quadratic Lie superalgebras. In this way, we obtain a numerical invariant of quadratic Lie superalgebras and…
Reductive W-algebras which are generated by bosonic fields of spin-1, a single spin-2 field and fermionic fields of spin-3/2 are classified. Three new cases are found: a `symplectic' family of superconformal algebras which are extended by…
We classify the 6-dimensional Lie algebras that can be endowed with an abelian complex structure and parameterize, on each of these algebras, the space of such structures up to holomorphic isomorphism.
We study complex projective varieties that parametrize (finite-dimensional) filiform Lie algebras over C, using equations derived by Millionshchikov. In the infinite-dimensional case we concentrate our attention on N-graded Lie algebras of…
We classify hom-Lie structures with nilpotent twisting map on $3$-dimensional complex Lie algebras, up to isomorphism, and classify all degenerations in such family. The ideas and techniques presented here can be easily extrapolated to…