On Multiple Polynomials of Capelli Type

On Multiple Polynomials of Capelli Type

This paper deals with the class of Capelli polynomials in free associative algebra F{Z} (where F is an arbitrary field, Z is a countable set) generalizing the construction of multiple Capelli polynomials. The fundamental properties of the introduced Capelli polynomials are provided. In particular, d...

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Bibliographic Details
Main Authors: S.Y. Antonov, A.V. Antonova
Format: Article
Language:Russian
Published: Kazan Federal University 2016-03-01
Series:Učënye Zapiski Kazanskogo Universiteta: Seriâ Fiziko-Matematičeskie Nauki
Subjects:
matrix algebra
Capelli polynomial
polynomial identity
free associative algebra
symmetric group
standard polynomial
T -idea
Online Access:http://kpfu.ru/portal/docs/F1262480853/158_1_phys_mat_1.pdf
Description
Summary:This paper deals with the class of Capelli polynomials in free associative algebra F{Z} (where F is an arbitrary field, Z is a countable set) generalizing the construction of multiple Capelli polynomials. The fundamental properties of the introduced Capelli polynomials are provided. In particular, decomposition of the Capelli polynomials by means of the same type of polynomials is shown. Furthermore, some relations between their T -ideals are revealed. A connection between double Capelli polynomials and Capelli quasi-polynomials is established.
ISSN:2541-7746
2500-2198

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