We point out how suitable algebraic n-valued groups (in the sense of Buchstaber) give rise, in a reasonably canonical manner, to algebraic groups. This is proved using the “group configuration theorem” of Hrushovski. In particular this applies to all algebraic 2-valued groups.

The purpose of this article is to prove an explicit invariant trace formula. In the preceding paper [l(j)] , we studied two families of invariant distributions. Now we shall exhibit these distributions as terms on the two sides of the invariant trace formula. We refer the reader to the introduction of [1 (j)], which contains a general discussion of the problem. In this introduction, we shall de...

We generalize to the case of a symmetric variety the construction of the enveloping semigroup of a semisimple algebraic group due to E.B. Vinberg, and we establish a connection with the wonderful completion of the associated adjoint symmetric variety due to C. De Concini and C.

This paper is about the question whether a cycle in the l-adic cohomology of a smooth projective variety over Q, which is algebraic over almost all finite fields Fp, is also algebraic over Q. We use ultraproducts respectively nonstandard techniques in the sense of A. Robinson, which the authors applied systematically to algebraic geometry in [BS07] and [BS08]. We give a reformulation of the que...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv CHAPTER

The purpose of this paper is to introduce an algebraic cohomology and formal deformation theory of left alternative algebras. Connections to some other algebraic structures are given also.

Let G be a finite group. The unit sphere in a finitedimensional orthogonal G-representation motivates the definition of homotopy representations, due to tom Dieck. We introduce an algebraic analogue and establish its basic properties, including the Borel–Smith conditions and realization by finite G-CW-complexes.

PROPs and Lawvere categories are related notions adapted to the study of algebraic structures borne by an object in a category, but whereas PROPs are symmetric monoidal, Lawvere categories are cartesian. This paper formulates the connection between the two notions using Lack’s technique for composing PROPs via distributive laws. We show Lawvere categories can be seen as resulting from a distrib...

In the study of geometric objects that arise naturally, the main tools are either groups or equations. In the first case, powerful algebraic methods are available and enable one to solve many deep problems. While algebraic methods are still important in the second case, analytic methods play a dominant role, especially when the defining equations are transcendental. Indeed, even in the situatio...

We show that if f and g are transcendental entire functions such that f(g) = g(f), then f satisfies an algebraic differential equation if and only if g does.