Israel Moiseevich Gelfand Vladimir Retakh, Coordinating Editor
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چکیده
Gelfand with grandaughter. Israel Moiseevich Gelfand, a mathematician compared by Henri Cartan to Poincaré and Hilbert, was born on September 2, 1913, in the small town of Okny (later Red Okny) near Odessa in the Ukraine and died in New Brunswick, New Jersey, USA, on October 5, 2009. Nobody guided Gelfand in his studies. He attended the only school in town, and his mathematics teacher could offer him nothing except encouragement—and this was very important. In Gelfand’s own words: “Offering encouragement is a teacher’s most important job.” In 1923 the family moved to another place and Gelfand entered a vocational school for chemistry lab technicians. However, he was expelled in the ninth grade as a son of a “bourgeois element” (“netrudovoi element” in Soviet parlance)—his father was a mill manager. After that Gelfand (he was sixteen and a half at that time) decided to go to Moscow, where he had some distant relatives. Until his move to Moscow in 1930, Gelfand lived in total mathematical isolation. The only books
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ar X iv : q - a lg / 9 70 10 08 v 2 4 F eb 1 99 7 FACTORIZATION OF DIFFERENTIAL OPERATORS , QUASIDETERMINANTS , AND NONABELIAN TODA FIELD EQUATIONS
We integrate nonabelian Toda field equations [Kr] for root systems of types A, B, C, for functions with values in any associative algebra. The solution is expressed via quasideterminants introduced in [GR1],[GR2], [GR4]. In the appendix we review some results concerning noncommutative versions of other classical integrable equations.
متن کاملCohomology in nonunitary representations of semisimple Lie groups (the group U(2, 2))
We suggest a method of constructing special nonunitary representations of semisimple Lie groups using representations of Iwasawa subgroups. As a typical example, we study the group U(2, 2).
متن کاملGelfand on mathematics and neurophysiology
It is well known that Gelfand’s scientific interests were not limited to mathematics. One of non-mathematical field where Israel Moiseevich Gelfand worked was neurophysiology. In late 1950s, he organized neurophysiological seminar and few years later he spearheaded two neurophysiological research groups: one at the Institute of Biophysics (after 1967, this group moved to the Institute for the P...
متن کاملNoncommutative Vieta Theorem and Symmetric Functions
There are two ways to generalize basic constructions of commutative algebra for a noncommutative case. More traditional way is to define commutative functions like trace or determinant over noncommuting variables. Beginning with [6] this approach was widely used by different authors, see for example [5], [15], [14], [12], [11], [7]. However, there is another possibility to work with purely nonc...
متن کاملHILBERT SERIES OF QUADRATIC ALGEBRAS ASSOCIATED WITH PSEUDO-ROOTS OF NONCOMMUTATIVE POLYNOMIALS Israel Gelfand, Sergei Gelfand,Vladimir Retakh,
The quadratic algebras Qn are associated with pseudo-roots of noncommutative polynomials. We compute the Hilbert series of the algebras Qn and of the dual algebras Q ! n. Introduction Let P (x) = x−a1x n−1 + · · ·+(−1)an be a polynomial over a ring R. Two classical problems concern the polynomial P (x): nvestigation of the solutions of the equation P (x) = 0 and the decomposition of P (x) into ...
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تاریخ انتشار 2012