Given an affine domain of Gelfand–Kirillov dimension 2 over an algebraically closed field, it is shown that the centralizer of any non-scalar element of this domain is a commutative domain of Gelfand–Kirillov dimension 1 whenever the domain is not polynomial identity. It is shown that the maximal subfields of the quotient division ring of a finitely graded Goldie algebra of Gelfand– Kirillov di...

In this paper, we first derive some results by using the Gelfand spectrum and spectrum in FLM algebras. Then, the characterizations of multiplicative linear mappings are also discussed in these algebras.

We define the (second) Adler-Gelfand-Dickey Poisson structure on differential operators over an elliptic curve and classify symplectic leaves of this structure. This problem turns out to be equivalent to classification of coadjoint orbits for double loop algebras, conjugacy classes in loop groups, and holomorphic vector bundles over the elliptic curve. We show that symplectic leaves have a fini...

Abstract We consider the Cauchy problem for a third-order evolution operator P with ( t , x )-depending coefficients and complex-valued lower-order terms. assume initial data to be Gevrey regular an exponential decay at infinity, that is, belong some Gelfand–Shilov space of type $${\mathscr {S}}$$ S . Under s...

We consider the non-linear spatially homogeneous Landau equation with Maxwellian molecules in a close-to-equilibrium framework and show that the Cauchy problem for the fluctuation around the Maxwellian equilibrium distribution enjoys a Gelfand-Shilov regularizing effect in the class S 1/2 1/2(R ), implying the ultra-analyticity of both the fluctuation and its Fourier transform, for any positive...

The Harish-Chandra homomorphism is due to [Harish-Chandra 1951]. Attention to universal modules with highest weights is in ]Harish-Chandra 1951], [Cartier 1955], as well as [Verma 1968], [BernsteinGelfand-Gelfand 1971a], [Bernstein-Gelfand-Gelfand 1971b], [Bernstein-Gelfand-Gelfand 1975]. See also [Jantzen 1979]. [1℄ We treat sl(2) in as simple a style as possible, to highlight ideas. Then sl(3...

I construct a correspondence between the Schubert cycles on the variety of complete flags in Cn and some faces of the Gelfand-Zetlin polytope associated with the irreducible representation of SLn(C) with a strictly dominant highest weight. The construction is based on a geometric presentation of Schubert cells by Bernstein–Gelfand– Gelfand [2] using Demazure modules. The correspondence between ...