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Full-Text Articles in Physical Sciences and Mathematics
A Comparison Theorem For The Topological And Algebraic Classification Of Quaternionic Toric 8-Manifolds, Piotr Runge
A Comparison Theorem For The Topological And Algebraic Classification Of Quaternionic Toric 8-Manifolds, Piotr Runge
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
In order to discuss topological properties of quaternionic toric 8-manifolds, we introduce the notion of an algebraic morphism in the category of toric spaces. We show that the classification of quaternionic toric 8-manifolds with respect to an algebraic isomorphism is finer than the oriented topological classification. We construct infinite families of quaternionic toric 8-manifolds in the same oriented homeomorphism type but algebraically distinct. To prove that the elements within each family are of the same oriented homeomorphism type, and that we have representatives of all such types of a quaternionic toric 8-manifold, we present and use a method of evaluating …
Symmetry Reduction Of Quasi-Free States, Charles G. Torre
Symmetry Reduction Of Quasi-Free States, Charles G. Torre
All Physics Faculty Publications
Given a group-invariant quasi-free state on the algebra of canonical commutation relations (CCR), we show how group averaging techniques can be used to obtain a symmetry-reduced CCR algebra and reduced quasi-free state. When the group is compact, this method of symmetry reduction leads to standard results which can be obtained using other methods. When the group is noncompact, the group averaging prescription relies on technically favorable conditions which we delineate. As an example, we consider symmetry reduction of the usual vacuum state for a Klein–Gordon field on Minkowski spacetime by a noncompact subgroup of the Poincaré group consisting of a …
The Classification Of Simple Lie Algebras In Maple, D. Russell Sadler
The Classification Of Simple Lie Algebras In Maple, D. Russell Sadler
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Lie algebras are invaluable tools in mathematics and physics as they enable us to study certain geometric objects such as Lie groups and differentiable manifolds. The computer algebra system Maple has several tools in its Lie Algebras package to work with Lie algebras and Lie groups. The purpose of this paper is to supplement the existing software with tools that are essential for the classification of simple Lie algebras over C.
In particular, we use a method to find a Cartan subalgebra of a Lie algebra in polynomial time. From the Cartan subalgebra we can compute the corresponding root system. …