Efim Zelmanov
Encyclopedia
Efim Isaakovich Zelmanov is a Russian mathematician
, known for his work on combinatorial problems in nonassociative algebra and group theory
, including his solution of the restricted Burnside problem. He was awarded a Fields Medal
at the International Congress of Mathematicians
in Zürich
in 1994.
Zelmanov was born into a Jewish family in Khabarovsk
, Russia. He obtained doctoral degree at Novosibirsk State University
in 1980, and a higher degree at Leningrad State University in 1985. He had a position in Novosibirsk until 1987, when he left the Soviet Union.
In 1990 he moved to the United States
, becoming a professor at the University of Wisconsin–Madison
. He was at the University of Chicago
in 1994/5, then at Yale University
. As of 2002, he is a professor at the University of California, San Diego
.
Zelmanov's early work was on Jordan algebra
s in the case of infinite dimensions. He was able to show that Glennie's identity in a certain sense generates all identities that hold. He then showed that the Engel identity for Lie algebra
s implies nilpotence, in the case of infinite dimensions.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, known for his work on combinatorial problems in nonassociative algebra and group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
, including his solution of the restricted Burnside problem. He was awarded a Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
at the International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
in Zürich
Zürich
Zurich is the largest city in Switzerland and the capital of the canton of Zurich. It is located in central Switzerland at the northwestern tip of Lake Zurich...
in 1994.
Zelmanov was born into a Jewish family in Khabarovsk
Khabarovsk
Khabarovsk is the largest city and the administrative center of Khabarovsk Krai, Russia. It is located some from the Chinese border. It is the second largest city in the Russian Far East, after Vladivostok. The city became the administrative center of the Far Eastern Federal District of Russia...
, Russia. He obtained doctoral degree at Novosibirsk State University
Novosibirsk State University
Novosibirsk State University was founded in May 1959 in the USSR by Soviet academicians Mikhail Alekseevich Lavrentiev, Sergei Lvovich Sobolev and Sergey Alekseyevich Khristianovich in a program of establishing a Siberian branch of the USSR Academy of Sciences...
in 1980, and a higher degree at Leningrad State University in 1985. He had a position in Novosibirsk until 1987, when he left the Soviet Union.
In 1990 he moved to the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
, becoming a professor at the University of Wisconsin–Madison
University of Wisconsin–Madison
The University of Wisconsin–Madison is a public research university located in Madison, Wisconsin, United States. Founded in 1848, UW–Madison is the flagship campus of the University of Wisconsin System. It became a land-grant institution in 1866...
. He was at the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
in 1994/5, then at Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
. As of 2002, he is a professor at the University of California, San Diego
University of California, San Diego
The University of California, San Diego, commonly known as UCSD or UC San Diego, is a public research university located in the La Jolla neighborhood of San Diego, California, United States...
.
Zelmanov's early work was on Jordan algebra
Jordan algebra
In abstract algebra, a Jordan algebra is an algebra over a field whose multiplication satisfies the following axioms:# xy = yx # = x ....
s in the case of infinite dimensions. He was able to show that Glennie's identity in a certain sense generates all identities that hold. He then showed that the Engel identity for Lie algebra
Lie algebra
In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...
s implies nilpotence, in the case of infinite dimensions.