Group automorphisms of the n-torus
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# Group automorphisms of the n-torus a representation theorem and some applications by Jerrill Douglas Kerrick

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Published .
Written in English

### Subjects:

• Ergodic theory.

## Book details:

Edition Notes

The Physical Object ID Numbers Statement by Jerrill Douglas Kerrick. Pagination [6], 106 leaves, bound ; Number of Pages 106 Open Library OL14242736M

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Let V = (V, Y, 1, ω) b e a simple v ertex op erator algebra and G a group of automorphisms of V (cf. [FLM]). Assume that G is a ﬁnite-dimensional compact Lie group and that the.   J. D. Kerrick, Group automorphisms of the n-torus: a representation theorem and some applications. Ph.D. Dissertation, Department of Mathematics, Oregon State University, Google ScholarCited by: 1. A maximal torus in the special unitary group SU(n) ⊂ U(n) is just the intersection of T and SU(n) which is a torus of dimension n − 1. A maximal torus in the special orthogonal group SO(2 n) is given by the set of all simultaneous rotations in any fixed choice of n pairwise orthogonal planes (i.e., two dimensional vector spaces). The Automorphism Group of a Variety with Torus Action of Complexity One. We denote the group of weak automorphisms of X by. Bir 2 (X). F is the n .

Given any group in general, the outer automorphism group consists of all the automorphisms of, modulo inner automorphisms. Outer automorphism groups of (finitely-generated, non-abelian) free groups have a particularly geometric flavour, since they may be thought of in terms of their action on a graph with fundamental group, i.e. (or e.g.) a. Groups and Manifolds: Lectures for Physicists with Examples in Mathematica Pietro Giuseppe Fre Groups and Manifolds is an introductory, yet a complete self-contained course on mathematics of symmetry: group theory and differential geometry of symmetric spaces, with a variety of examples for physicists, touching briefly also on super-symmetric. Series Editor ISAAK MAYERGOYZ, in Numerical Methods in Electromagnetism, This book reflects the unique expertise, extensive experience, and strong interests of the authors in the computational aspects of electromagnetism. The unique feature of this book is its broad scope and unbiased treatment of finite element, finite difference, and integral equation techniques. cial degenerations equivariant under a compact group of automorphisms, then M admits a Kahler-Einstein metric. This is a strengthening of the solution of the Yau-Tian-Donaldson conjecture for Fano manifolds by Chen-Donaldson-Sun [17], and can be used to obtain new examples of Kahler-Einstein by:

It is usually used for an algebraic group which is, over the algebraic closure, isomorphic to the direct sum of n copies of the multiplicative group. "Complex torus" is usually used for a compact, complex Lie group, necessarily then C^n modulo a lattice. In geometry, a torus (pl. tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a ring torus or simply torus if the ring shape is implicit.. When the axis is tangent to the circle, the resulting surface is called a horn. Consider a discrete group Γ and an element f in the integral group ring ZΓ. Then Γ acts from the left on the discrete additive group ZΓ/ZΓf by automorphisms of groups. Dualizing, we obtain a left Γ-action on the compact Pontrjagin dual group Xf = Z\Γ/ZΓfby continuous automorphisms of groups. By deﬁnition, Xf is a closed. Let Γ be the group generated by the e ij and Γ k with relations e ij −1 g e ij = ψ ij (g) for g in Γ i and e ik = e jk e ij g ijk. if i \rightarrow j \rightarrow k. For a fixed vertex i 0, the edge-path group Γ(i 0) is defined to be the subgroup of Γ generated by all products g 0 .