|
Anatoly Shirshov
Anatoly Illarionovich Shirshov (Анато́лий Илларио́нович Ширшо́в, 8 August 1921, Kolyvan, Novosibirsk Oblast – 28 February 1981, Novosibirsk) was a Soviet mathematician, known for his research on free Lie algebras. He proved the Shirshov–Witt theorem, which states that any Lie subalgebra of a free Lie algebra is itself a free Lie algebra. Life Anatoly was born on the 8th of August 1921 in the village Kolyvan near Novosibirsk. In 1939 he graduated from secondary school in the city of Aleysk of the Altai Territory and in the same year entered Tomsk University. After the first year, he transferred to the correspondence ("distance education" or "learning by mail") department and worked as a mathematics teacher in Aleysk. One of the streets of Aleisk is named after Anatoly Shirshov. In 1942 A. I. Shirshov volunteered for the front as part of 6th Rifle Corps of Siberian Volunteers. He fought on the West, Kalininsky, and 2nd Belorussian Fronts. He wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Novosibirsk Oblast
Novosibirsk Oblast (russian: Новосиби́рская о́бласть, ''Novosibirskaya oblast'') is a federal subject of Russia (an oblast) located in southwestern Siberia. Its administrative and economic center is the city of Novosibirsk. The population was 2,788,849 as of the 2018 Census. Geography Overview Novosibirsk Oblast is located in the south of the West Siberian Plain, at the foothills of low Salair ridge, between the Ob and Irtysh Rivers. The oblast borders Omsk Oblast in the west, Kazakhstan ( Pavlodar Province) in the southwest, Tomsk Oblast in the north, Kemerovo Oblast in the east, and Altai Krai in the south. The territory of the oblast extends for more than from west to east, and for over from north to south. The oblast is mainly plain; in the south the steppes prevail; in the north enormous tracts of woodland with great number of marshes prevail. There are many lakes, the largest ones located at the south. The majority of the rivers belo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Novosibirsk State University
Novosibirsk State University is a public research university located in Novosibirsk, Russia. The university was founded in 1958, on the principles of integration of education and science, early involvement of students with research activities and the engagement of leading scientists in its teaching programmes. As of 2022, Novosibirsk State University had 246th place in the rating of the QS World University Rankings, and was ranked #503 in the world by '' U.S. News & World Report'', and #801 in the world by World University Rankings by ''Times Higher Education''. History From the perspective of natural resources, Siberia has always been, and remains, the essential region for all of Russia. In the late 1950s, Siberia provided the country with 75% of its coal and possessed 80% of the nation's hydroelectric resources. Siberia became industrialized, but science then was largely of the applied variety and did not satisfy its needs. The USSR Academy of Sciences came to understand t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moscow State University Alumni
Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million residents within the city limits, over 17 million residents in the urban area, and over 21.5 million residents in the metropolitan area. The city covers an area of , while the urban area covers , and the metropolitan area covers over . Moscow is among the world's largest cities; being the most populous city entirely in Europe, the largest urban and metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow grew to become a prosperous and powerful city that served as the capital of the Grand Duchy that bears its name. When the Grand Duchy of Moscow evolved into the Tsardom of Russia, Moscow remained the political and economic center for most of the Tsardom's history. W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1981 Deaths
Events January * January 1 ** Greece enters the European Economic Community, predecessor of the European Union. ** Palau becomes a self-governing territory. * January 10 – Salvadoran Civil War: The FMLN launches its first major offensive, gaining control of most of Morazán and Chalatenango departments. * January 15 – Pope John Paul II receives a delegation led by Polish Solidarity leader Lech Wałęsa at the Vatican. * January 20 – Iran releases the 52 Americans held for 444 days, minutes after Ronald Reagan is sworn in as the 40th President of the United States, ending the Iran hostage crisis. * January 21 – The first DeLorean automobile, a stainless steel sports car with gull-wing doors, rolls off the production line in Dunmurry, Northern Ireland. * January 24 – An earthquake of magnitude in Sichuan, China, kills 150 people. Japan suffers a less serious earthquake on the same day. * January 25 – In South Africa the largest part of the town Laingsburg is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1921 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album '' 63/19'' by Kool A.D. * '' Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album ''Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Restricted Burnside Problem
The Burnside problem asks whether a finitely generated group in which every element has finite order must necessarily be a finite group. It was posed by William Burnside in 1902, making it one of the oldest questions in group theory and was influential in the development of combinatorial group theory. It is known to have a negative answer in general, as Evgeny Golod and Igor Shafarevich provided a counter-example in 1964. The problem has many refinements and variants (see bounded and restricted below) that differ in the additional conditions imposed on the orders of the group elements, some of which are still open questions. Brief history Initial work pointed towards the affirmative answer. For example, if a group ''G'' is finitely generated and the order of each element of ''G'' is a divisor of 4, then ''G'' is finite. Moreover, A. I. Kostrikin was able to prove in 1958 that among the finite groups with a given number of generators and a given prime exponent, there exists ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Efim Zelmanov
Efim Isaakovich Zelmanov (russian: Ефи́м Исаа́кович Зе́льманов; born 7 September 1955 in Khabarovsk) is a Russian-American 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, Soviet Union (now in Russia). He entered Novosibirsk State University in 1972, when he was 17 years old. He obtained a 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. In 2011, he became a professor at the Universit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Plane
In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines (namely, parallel lines) that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus ''any'' two distinct lines in a projective plane intersect at exactly one point. Renaissance artists, in developing the techniques of drawing in perspective, laid the groundwork for this mathematical topic. The archetypical example is the real projective plane, also known as the extended Euclidean plane. This example, in slightly different guises, is important in algebraic geometry, topology and projective geometry where it may be denoted variously by , RP2, or P2(R), among other notations. There are many other projective planes, both infinite, such as the complex projective pla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group (mathematics)
In mathematics, a group is a set and an operation that combines any two elements of the set to produce a third element of the set, in such a way that the operation is associative, an identity element exists and every element has an inverse. These three axioms hold for number systems and many other mathematical structures. For example, the integers together with the addition operation form a group. The concept of a group and the axioms that define it were elaborated for handling, in a unified way, essential structural properties of very different mathematical entities such as numbers, geometric shapes and polynomial roots. Because the concept of groups is ubiquitous in numerous areas both within and outside mathematics, some authors consider it as a central organizing principle of contemporary mathematics. In geometry groups arise naturally in the study of symmetries and geometric transformations: The symmetries of an object form a group, called the symmetry group of the ob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alternative Algebra
In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have *x(xy) = (xx)y *(yx)x = y(xx) for all ''x'' and ''y'' in the algebra. Every associative algebra is obviously alternative, but so too are some strictly non-associative algebras such as the octonions. The associator Alternative algebras are so named because they are the algebras for which the associator is alternating. The associator is a trilinear map given by : ,y,z= (xy)z - x(yz). By definition, a multilinear map is alternating if it vanishes whenever two of its arguments are equal. The left and right alternative identities for an algebra are equivalent toSchafer (1995) p. 27 : ,x,y= 0 : ,x,x= 0. Both of these identities together imply that : ,y,x= , x, x+ , y, x- , x+y, x+y= , x+y, -y= , x, -y- , y, y= 0 for all x and y. This is equivalent to the '' flexible identity''Schafer (1995) p. 28 :(xy)x = x(yx). The associator of an a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jordan Algebra
In abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms: # xy = yx (commutative law) # (xy)(xx) = x(y(xx)) (). The product of two elements ''x'' and ''y'' in a Jordan algebra is also denoted ''x'' ∘ ''y'', particularly to avoid confusion with the product of a related associative algebra. The axioms imply that a Jordan algebra is power-associative, meaning that x^n = x \cdots x is independent of how we parenthesize this expression. They also imply that x^m (x^n y) = x^n(x^m y) for all positive integers ''m'' and ''n''. Thus, we may equivalently define a Jordan algebra to be a commutative, power-associative algebra such that for any element x, the operations of multiplying by powers x^n all commute. Jordan algebras were first introduced by to formalize the notion of an algebra of observables in quantum mechanics. They were originally called "r-number systems", but were renamed "Jordan algebras" by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Algebra
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identity. The Lie bracket of two vectors x and y is denoted ,y/math>. The vector space \mathfrak g together with this operation is a non-associative algebra, meaning that the Lie bracket is not necessarily associative. Lie algebras are closely related to Lie groups, which are groups that are also smooth manifolds: any Lie group gives rise to a Lie algebra, which is its tangent space at the identity. Conversely, to any finite-dimensional Lie algebra over real or complex numbers, there is a corresponding connected Lie group unique up to finite coverings ( Lie's third theorem). This correspondence allows one to study the structure and classification of Lie groups in terms of Lie algebras. In physics, Lie groups appear as symmetry grou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
