To the jubilee of Professor Yuriy Drozd
This is a special issue of the journal devoted to the jubilee of the outstanding Ukrainian mathematician, one of the founder of our journal Professor Yuriy Drozd.
Збережено в:
| Дата: | 2005 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/156613 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | To the jubilee of Professor Yuriy Drozd // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — англ. |
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irk-123456789-1566132019-08-31T12:47:42Z To the jubilee of Professor Yuriy Drozd This is a special issue of the journal devoted to the jubilee of the outstanding Ukrainian mathematician, one of the founder of our journal Professor Yuriy Drozd. 2005 Article To the jubilee of Professor Yuriy Drozd // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — англ. 1726-3255 http://dspace.nbuv.gov.ua/handle/123456789/156613 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
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English |
| description |
This is a special issue of the journal devoted to the jubilee of the
outstanding Ukrainian mathematician, one of the founder of our journal
Professor Yuriy Drozd. |
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Article |
| title |
To the jubilee of Professor Yuriy Drozd |
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To the jubilee of Professor Yuriy Drozd Algebra and Discrete Mathematics |
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To the jubilee of Professor Yuriy Drozd |
| title_full |
To the jubilee of Professor Yuriy Drozd |
| title_fullStr |
To the jubilee of Professor Yuriy Drozd |
| title_full_unstemmed |
To the jubilee of Professor Yuriy Drozd |
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to the jubilee of professor yuriy drozd |
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Інститут прикладної математики і механіки НАН України |
| publishDate |
2005 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/156613 |
| citation_txt |
To the jubilee of Professor Yuriy Drozd // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — англ. |
| series |
Algebra and Discrete Mathematics |
| first_indexed |
2025-07-14T09:00:20Z |
| last_indexed |
2025-07-14T09:00:20Z |
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1837612265713434624 |
| fulltext |
This is a special issue of the journal devoted to the jubilee of the
outstanding Ukrainian mathematician, one of the founder of our journal
Professor Yuriy Drozd.
Yuriy Drozd was born on the 15th of October, 1944 in Kyiv, in a fam-
ily of officers, participants of the II World War (his mother was a doctor,
his father was an engineer). He was delighted in mathematics still at
school, due to his teacher, Asia Aronivna Horon. By the way, three of
her former pupils became Doctors of Sciences (the highest scientific degree
in the former Soviet Union); it is interesting that all three of them were
working in algebra: M.Kargapolov, A.Roiter and Y.Drozd. In 1961 Yuriy
got the first prize at the 1st Ukrainian mathematical competition, and at
the first All-Russian mathematical competition. The same year he en-
tered Kyiv Taras Shevchenko University, Department of Mechanics and
Mathematics. In 1966 he graduated from the University with honours.
His advisor at the University was A.Roiter. Collaboration with A.Roiter
and V.Kirichenko was a valuable experience of the scientific research for
the young mathematician. The main result of his Diploma work (Master
Thesis) was a criterion of finiteness of the set of indecomposable represen-
tations for cubic rings. It was published in "Proceedings of the Academy
F Editorial information
of Sciences of the USSR" and was important for the future development
of the theory of integral representations of rings.
In 1966 Yuriy Drozd entered a graduate study program at the Institute
of Mathematics of the Academy of Sciences of Ukraine. His advisor there
was one of the most prominent Soviet mathematicians Igor Shafarevich.
In February 1969 Yuriy accomplished his graduate study and since then
he was working at the Kyiv Taras Shevchenko University, Department
of Mechanics and Mathematics, Division of Algebra and Mathematical
Logic. There he followed a long track, form an assistant till a full pro-
fessor and Head of the Division (1980-1998). In 1970 he presented his
Candidate (Ph.D.) Thesis "On Several Questions of the Theory of Inte-
gral Representations" at the Steklov Mathematical Institute in Moscow.
The results of this thesis, such as a criterion of finiteness of the set of
indecomposable representations for commutative orders, structure theory
of hereditary and Bassian orders, new results on the structure of genera,
took since then a central place in the whole theory of integral representa-
tions.
In the following years the scientific interests of Yuriy Drozd broadened.
He started his works on a new area, the theory of the so called "matrix
problems." Soon he proved one of the main results here, the "tame-wild di-
chotomy," i.e. the theorem that every finite dimensional algebra is either
representation tame or representation wild. This result was the origin
of a series of works of specialists through the world. Several conferences
were specially devoted to this "tame-wild subject." Yuriy Drozd also im-
plemented the matrix techniques into new areas, such as the multiplicative
theory of ideals and others. In 1981 he presented to the Leningrad Uni-
versity his Doctor of Sciences Thesis "Matrix Methods in the Theory of
Representations and Rings".
In eighties Yuriy Drozd initiated at the Kyiv University investigations
of representations of Lie algebras and groups. In his first paper in this field
"On representations of the Lie Algebra sl(2)" he applied matrix methods to
study of these representations. Further, in collaboration with S.Ovsienko
and V.Futorny, he studied new classes of representations, such as weight
representations, Gelfand-Zetlin representations, representations of gen-
eral position of "mixed" linear groups, etc. Now the achievements of Kyiv
mathematicians in these topics are well known and highly appreciated.
The downfall of the USSR and of the Iron Curtain opened a new stage
in the scientific biography of Yuriy Drozd. In 1989 he was able for the
first time to participate in a scientific conference in the West (it was a
meeting of the London Mathematical Society), though he had got invi-
tations to such conferences regularly during more than 15 years before.
Further on such visits became usual. From 1992 he was a member of
the Scientific Committee of the International Conferences on Represen-
tations of Algebras (ICRA), which take place every two years. In 1997
he organized an International Conference on Representation Theory and
Computer Algebra in Kyiv.
From 1990 Yuriy Drozd started his fruitful collaboration with his Ger-
man colleague G.-M.Greuel on investigation of Cohen-Macaulay modules.
In about two or three years they completely described representation types
of one-dimensional Cohen-Macaulay rings. For Yuriy it was, in a since,
a return to his youth, since this topic is a variant of the theory of inte-
gral representations of rings. Further they solved the analogous question
for vector bundles over projective curves and for a wide class of two-
dimensional Cohen-Macaulay rings. Since 1998 Yuriy Drozd started col-
laboration with another German mathematician, H.-J.Baues, in algebraic
topology, which was a completely new area for him. Applying the matrix
techniques, they advanced well in classification of stable homotopy types
of polyhedra.
These topics led Yuriy Drozd to the theory of derived categories. With
his disciples V.Bekkert and I.Burban he extend to these categories the
tame-wild dichotomy and gave a complete classification of complexes in
derived categories of a wide class of rings as well as for tame projective
curves.
Now he is successfully continuing these investigations. They were
published in more than 90 papers and served as a basis for 25 Candi-
date (Ph.D.) Theses of his students (three of them are now Doctors of
Sciences). Yuriy Drozd is the author of several University textbooks. Es-
pecially the book "Finite Dimensional Algebras" by him and V.Kirichenko
was translated by Springer-Verlag into English and is now the most used
by students through the world. Yuriy Drozd was a visiting professor at the
Universities of Strasbourg, Kaiserslautern, Torun, Santa Barbara, Upp-
sala. He gave survey talks as invited lector at the international confer-
ences and seminars in Japan, Germany, Great Britain, USA, Canada,
France, Mexico, Spain, Brazil.
V. I. Andriychuk, V.M. Futorny,
R.I. Grigorchuk, P. M. Gudyvok,
V.V. Kirichenko, M.Ya. Komarnitsky,
L.A. Kurdachenko, V.V. Lyubashenko,
B.V. Novikov, A.P. Petravchuk,
V.I. Sushchansky, V. M. Usenko,
P. D. Varbanets.
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