Isotropy of Algebraic Theories

Isotropy theorem for cosmological Yang-Mills theories

We consider homogeneous non-Abelian vector fields with general potential terms in an expanding universe. We find a mechanical analogy with a system of N interacting particles (with N the dimension of the gauge group) moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of a general...

Algebraic theories

We presents the algebraic theories over an arbitrary monoid, main properties and calculus rules. Ordered, rationaly closed and ω-continuous theories on one hand and matrix and complete matrix theories on the other hand are the presentation main subjects. Some examples comming from algebra and computer science finish this paper.

Extension of Algebraic Theories

The algebraic theories of Lawvere are extended in a natural way to small complete categories. These categories exhibit not only the operations and identities, but some of the homomorphisms, functions, objects and constructions which are encountered when working within the algebraic categories associated with the theories. The category of extended theories is isomorphic to the original category ...

Cohomology of Algebraic Theories

Algebraic Realization for Cyclic Group Actions with One Isotropy Type

Suppose G is a cyclic group and M a closed smooth G– manifold with exactly one isotropy type. We will show that there is a nonsingular real algebraic G–variety X which is equivariantly diffeomorphic to M and all G–vector bundles over X are strongly algebraic.