Algebras of Free Holomorphic Functions and Localizations

Student: Syrtseva Ksenia

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2017

The notion of localization was discovered several times in different contexts and was named differently. The definition used in our paper was introduced by J. L. Taylor in 1973. He also investigated a more narrow scope of algebras, namely, free analytic algebras. We deal with algebras which can be considered as "algebras of holomophic functions on the free polydisk and on the free ball". The aim of our paper is to figure out whether these algebras are localizations of free algebra and whether they are free analytic algebras. In addition, we show that the Arens-Michael free product saves the properties "being localization of free algebra" and "being free analytic algebra".

Student Theses at HSE must be completed in accordance with the University Rules and regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.

Search all student theses