Related papers: A simple E8 construction
The explicit list of all almost factorizable Lie bialgebra structures on real absolutely simple Lie algebras is given.
A new structure, based on joining copies of a group by means of a \emph{twist}, has recently been considered to describe the brackets of the two exceptional real Lie algebras of type $G_2$ in a highly symmetric way. In this work we show…
We construct motivic $\ell$-adic representations of $\GQ$ into exceptional groups of type $E_7,E_8$ and $G_2$ whose image is Zariski dense. This answers a question of Serre. The construction is uniform for these groups and uses the…
We construct and study fields F with the property that F has infinitely many extensions of some fixed degree, but E*/(E*)^n is finite for every finite extension E of F and every n>0.
We give an explicit characterization of solvable factors in factorizations of finite classical groups of Lie type. This completes the classification of solvable factors in factorizations of almost simple groups, finishing the program…
Attempts to extend our previous work using the octonions to describe fundamental particles lead naturally to the consideration of a particular real, noncompact form of the exceptional Lie group E6, and of its subgroups. We are therefore led…
The Berezin quantization on a simply connected homogeneous K\"{a}hler manifold, which is considered as a phase space for a dynamical system, enables a description of the quantal system in a (finite-dimensional) Hilbert space of holomorphic…
The generalized projection-tensor geometry introduced in an earlier paper is extended. A compact notation for families of projected objects is introduced and used to summarize the results of the previous paper and obtain fully projected…
In this expository paper, we first review the classification of the restricted simple Lie algebras in characteristic different from 2 and 3 and then we describe their infinitesimal deformations. We conclude by indicating some possible…
We construct harmonic morphisms on the compact simple Lie group G2. The construction uses eigenfamilies in a representation theoretic scheme.
The $E_8$ root lattice can be constructed from the modular curve $X(13)$ by the invariant theory for the simple group $\text{PSL}(2, 13)$. This gives a different construction of the $E_8$ root lattice. It also gives an explicit construction…
We prove the existence of certain rationally rigid triples E8 in good characteristic and thereby show that these groups over the prime field occur as Galois groups over the field of rational numbers. We show that these triples give rise to…
We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras. Lie bialgebras are examples of generalized Lie bialgebras. Moreover, we prove that the last ones can be considered as the infinitesimal…
Starting from basic identities of the group E8, we perform progressive reductions, namely decompositions with respect to the maximal and symmetric embeddings of E7xSU(2) and then of E6xU(1). This procedure provides a systematic approach to…
The decomposition problem of the enveloping algebra of a simple Lie algebra is reconsidered combining both the analytical and the algebraic approach, showing its relation with the internal labelling problem with respect to a nilpotent…
The group gradings on the symmetric composition algebras over arbitrary fields are classified. Applications of this result to gradings on the exceptional simple Lie algebras are considered too.
We describe and analyze a new construction that produces new Eulerian lattices from old ones. It specializes to a construction that produces new strongly regular cellular spheres (whose face lattices are Eulerian). The construction does not…
We construct a central Lie group extension for the Lie group of compactly supported sections of a Lie group bundle over a sigma-compact base manifold. This generalises a result of the paper "Central extensions of groups of sections" by Neeb…
We introduce the universal Euler characteristic of orbit space definable groupoids, a class of groupoids containing cocompact proper Lie groupoids as well as translation groupoids associated to proper definable group actions. We show that…
We discuss the universal orbifold Euler characteristic and generalized orbifold Euler characteristics corresponding to finitely generated groups $A$ (the $A$-Euler characteristics). We show that the collection of all $A$-Euler…