Background
Sabinin, Lev Vasilevich was born on June 21, 1932 in Voronezh, Russia, Union of the Soviet Socialist Republics. Son of Vasiliy Nicolaevich and Ludmila Afanasievna (Vasilieva) Sabinin.
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book
Smooth Quasigroups and Loops (Mathematics and Its Applications)
(During the last twenty-five years quite remarkable relati...)
During the last twenty-five years quite remarkable relations between nonas sociative algebra and differential geometry have been discovered in our work. Such exotic structures of algebra as quasigroups and loops were obtained from purely geometric structures such as affinely connected spaces. The notion ofodule was introduced as a fundamental algebraic invariant of differential geometry. For any space with an affine connection loopuscular, odular and geoodular structures (partial smooth algebras of a special kind) were introduced and studied. As it happened, the natural geoodular structure of an affinely connected space al lows us to reconstruct this space in a unique way. Moreover, any smooth ab stractly given geoodular structure generates in a unique manner an affinely con nected space with the natural geoodular structure isomorphic to the initial one. The above said means that any affinely connected (in particular, Riemannian) space can be treated as a purely algebraic structure equipped with smoothness. Numerous habitual geometric properties may be expressed in the language of geoodular structures by means of algebraic identities, etc.. Our treatment has led us to the purely algebraic concept of affinely connected (in particular, Riemannian) spaces; for example, one can consider a discrete, or, even, finite space with affine connection (in the form ofgeoodular structure) which can be used in the old problem of discrete space-time in relativity, essential for the quantum space-time theory.
http://www.amazon.com/gp/product/9401059217/?tag=2022091-20
Smooth Quasigroups and Loops (Mathematics and Its Applications)
(During the last twenty-five years quite remarkable relati...)
During the last twenty-five years quite remarkable relations between nonas sociative algebra and differential geometry have been discovered in our work. Such exotic structures of algebra as quasigroups and loops were obtained from purely geometric structures such as affinely connected spaces. The notion ofodule was introduced as a fundamental algebraic invariant of differential geometry. For any space with an affine connection loopuscular, odular and geoodular structures (partial smooth algebras of a special kind) were introduced and studied. As it happened, the natural geoodular structure of an affinely connected space al lows us to reconstruct this space in a unique way. Moreover, any smooth ab stractly given geoodular structure generates in a unique manner an affinely con nected space with the natural geoodular structure isomorphic to the initial one. The above said means that any affinely connected (in particular, Riemannian) space can be treated as a purely algebraic structure equipped with smoothness. Numerous habitual geometric properties may be expressed in the language of geoodular structures by means of algebraic identities, etc.. Our treatment has led us to the purely algebraic concept of affinely connected (in particular, Riemannian) spaces; for example, one can consider a discrete, or, even, finite space with affine connection (in the form ofgeoodular structure) which can be used in the old problem of discrete space-time in relativity, essential for the quantum space-time theory.
http://www.amazon.com/gp/product/0792359208/?tag=2022091-20
Lev Vasilevich Sabinin
Edit Profileeducator mathematics researcher
Education
Master of Science, Moscow University, 1955. Doctor of Philosophy, Moscow University, 1959. Doctor of Science, Kazan (Union of the Soviet Socialist Republics) University, 1972.
Career
Junior research fellow Institute of Mathematics, Novosibirsk, Union of the Soviet Socialist Republics, 1958-1960, senior research fellow Union of the Soviet Socialist Republics, 1960-1965. Reader Friendship of Nations University, Moscow, 1965-1972. Professor Ile-Ife (Nigeria) University, 1972-1974, Friendship of Nations University, Moscow, since 1974.
Lecturer Novosibirsk University, 1959-1961, reader, 1961-1965. Visiting professor Mathematics Institute, Universidad Nacional Autónoma de México, Mexico, 1995, Michoacan University, Mexico, 1996-1998. Extraordinary professor Quintana Reo University, Mexico, since 1998.
Achievements
Works
book
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Smooth Quasigroups and Loops (Mathematics and Its Applications)
(During the last twenty-five years quite remarkable relati...)
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Smooth Quasigroups and Loops (Mathematics and Its Applications)
(During the last twenty-five years quite remarkable relati...)
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Smooth Quasigroups and Loops (Mathematics and Its Applications)
Membership
Member Moscow Mathematics Society, Siberian Mathematics Society, American Mathematics Society, Mexico Mathematics Society, Mexico National Systems Researchers (level III).
Interests
Connections
Married Eugenia Sezgeevna Soboleva, April 24, 1955 (divorced May 1964). Children: Sergey, Ludmila. Married Larisa Viacheslavovna Sbitneva, September 13, 1969.
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Born
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Nationality
Russian -
Ethnicity
Education
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1955
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1959
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1972
Career
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1958 - 1960
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1965 - 1972
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1972 - 1974
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1974