The Fundamental Basis Theorem of Geometry from an algebraic point of view

37th International Conference on Quantum Probability and Related Topics

Bekbaev, U.^1

Department of Science in Engineering, Faculty of Engineering, International Islamic University Malaysia, P.O. Box 10, Kuala Lumpur

50728, Malaysia^1

关键词: Invariant differential operators;    New results;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/819/1/012013/pdf
DOI  :  10.1088/1742-6596/819/1/012013

来源: IOP

【 摘 要 】

An algebraic analog of the Fundamental Basis Theorem of geometry is offered with a pure algebraic proof involving the famous Waring's problem for polynomials. Unlike the geometry case the offered system of invariant differential operators is commuting, which is a new result even in the classical geometry of surfaces. Moreover the algebraic analog works in more general settings then does the Fundamental Basis Theorem of geometry.