Mathematics – Representation Theory
Scientific paper
2002-06-04
Mathematics
Representation Theory
10 pages
Scientific paper
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.
Litvinov Grigori
Maslov Viktor
Shpiz Grigori
No associations
LandOfFree
Idempotent (Asymptotic) Mathematics and the Representation Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Idempotent (Asymptotic) Mathematics and the Representation Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Idempotent (Asymptotic) Mathematics and the Representation Theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-96156