2002/06/04 by Grigori Litvinov, Litvinov, Grigori, V. P. Maslov +4
Computer Science · Mathematics · #22E99 #Computability, Logic, AI Algorithms #FOS: Mathematics #Representation Theory (math.RT) #Topological and Geometric Data Analysis #math.RT #msc:22E99
paper · pdf · doi:10.48550/arxiv.math/0206025
10 pages
arxiv created 2002/06/04 · openalex publication_date 2002/06/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A brief survey of some basic ideas of the so-called Idempotent Mathematics is presented; an "idempotent" version of the representation theory is discussed. The Idempotent Mathematics can be treated as a result of a dequantization of the traditional mathematics over numerical fields in the limit of the vanishing "imaginary Planck constant"; there is a correspondence, in the spirit of N. Bohr's correspondence principle, between constructions and results in traditional mathematics over the fields of real and complex numbers and similar constructions and results over idempotent semirings. In particular, there is an "idempotent" version of the theory of linear representations of groups. Some basic concepts and results of the "idempotent" representation theory are presented. In the framework of this theory the well-known Legendre transform can be treated as an idempotent version of the traditional Fourier transform. Some unexpected versions of the Engel theorem are given.