THE SYSTEM OF d-GENERATORS OF d-SKEW FIELD OF
Sp(n)-INVARIANT d-RATIONAL FUNCTIONS
Kobyljon Muminov1, Saidaxbor Juraboyev2
1National University of Uzbekistan named after Mirzo Ulugbek
Tashkent - 100174, UZBEKISTAN
2Fergana State University
Fergana - 150100, UZBEKISTAN

Abstract

Let $H^{n}$ be an $n$ dimensional (the left) vector space over the skew-field of quaternion numbers, and $Sp(n)$ be a group of symplectic transformations of $H^{n}$. Also, the skew-field of all $Sp(n)-$invariant non-commutative differential rational functions denoted by $\Re{{\left[\!\left[ x,\bar{x} \right]\!\right]}^{Sp\left( n \right)}}$. In the paper an explicit description of a finite generating system in the differential skew-field $\Re{{\left[\!\left[ x,\bar{x} \right]\!\right]}^{Sp\left( n \right)}}$.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 6
Year: 2022

DOI: 10.12732/ijam.v35i6.8

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