The classical Waring problem deals with expressing every natural number as a sum of g(k) k powers. Similar problems were recently studied in group theory, where we aim to present group elements as short products of values of a given word w 6= 1. In this paper we study this problem for Lie groups and Chevalley groups over infinite fields. We show that for a fixed word w 6= 1 and for a classical ...

Let $$\mathfrak {m}$$ be the Monster Lie algebra. We summarize several interrelated constructions of group analogs for . Our are Chevalley and Kac–Moody groups their generators relations.

Let G be a simply connected Chevalley group, and P =MN a maximal parabolic subgroup of G. Let n be the Lie algebra of N . A choice of Chevalley basis defines a Z-structure on n, The structure ofM orbits over Z on irreducible subquotients of n could be highly non-trivial, and very interesting as Bhargava [B] shows. In the first part of this paper we deal with this question in the case when G is ...

In the traditional approaches to Clifford algebras, the Clifford product is evaluated by recursive application of the product of a one-vector (span of the generators) on homogeneous i.e. sums of decomposable (Graßmann), multi-vectors and later extended by bilinearity. The Hestenesian ’dot’ product, extending the one-vector scalar product, is even worse having exceptions for scalars and the need...

Aclassic result of [Tannaka:1939], in the formulation of [Chevalley:1946], asserts that every compact subgroup of GLn(C) is the group of real points on an algebraic group defined over R. Chevalley introduced a more algebraic approach to the topic, but his underlying argument is not so different from Tannaka’s. The literature since then has followed one of two threads. One is algebraic (as in Ch...

We study the variety of actions of a fixed (Chevalley) group on arbitrary geodesic, Gromov hyperbolic spaces. In high rank we obtain a complete classification. In rank one, we obtain some partial results and give a conjectural picture.

We show that the Sylow 2-subgroups of nearly all Chevalley groups in even characteristic allow the definition of a check-character-system which detects all single and the most important double errors.

We compute the cobordism rings of the classifying spaces of a certain class of Chevalley groups. In the particular case of the general linear group, we prove that it is isomorphic to the Chow ring.

We define certain extensions of Jacobi groups A<sub>1</sub>, prove an analogue Chevalley theorem for their invariants, and construct a Dubrovin-Frobenius structure on its orbit space.