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Smooth components of Springer fibers

William Graham, R. Zierau (2011)

Annales de l’institut Fourier

This article studies components of Springer fibers for 𝔤𝔩 ( n ) that are associated to closed orbits of G L ( p ) × G L ( q ) on the flag variety of G L ( n ) , n = p + q . These components occur in any Springer fiber. In contrast to the case of arbitrary components, these components are smooth varieties. Using results of Barchini and Zierau we show these components are iterated bundles and are stable under the action of a maximal torus of G L ( n ) . We prove that if ℒ is a line bundle on the flag variety associated to a dominant weight, then the higher...

Solution of Belousov's problem

Maks A. Akivis, Vladislav V. Goldberg (2001)

Discussiones Mathematicae - General Algebra and Applications

The authors prove that a local n-quasigroup defined by the equation x n + 1 = F ( x ₁ , . . . , x ₙ ) = ( f ₁ ( x ₁ ) + . . . + f ₙ ( x ₙ ) ) / ( x ₁ + . . . + x ₙ ) , where f i ( x i ) , i,j = 1,...,n, are arbitrary functions, is irreducible if and only if any two functions f i ( x i ) and f j ( x j ) , i ≠ j, are not both linear homogeneous, or these functions are linear homogeneous but f i ( x i ) / x i ≠ f j ( x j ) / x j . This gives a solution of Belousov’s problem to construct examples of irreducible n-quasigroups for any n ≥ 3.

Solution of distributive-like quasigroup functional equations

Fedir M. Sokhatsky, Halyna V. Krainichuk (2012)

Commentationes Mathematicae Universitatis Carolinae

We are investigating quasigroup functional equation classification up to parastrophic equivalence [Sokhatsky F.M.: On classification of functional equations on quasigroups, Ukrainian Math. J. 56 (2004), no. 4, 1259–1266 (in Ukrainian)]. If functional equations are parastrophically equivalent, then their functional variables can be renamed in such a way that the obtained equations are equivalent, i.e., their solution sets are equal. There exist five classes of generalized distributive-like quasigroup...

Some aspects of nuclear vector groups

Lydia Außenhofer (2001)

Studia Mathematica

In [2] W. Banaszczyk introduced nuclear groups, a Hausdorff variety of abelian topological groups which is generated by all nuclear vector groups (cf. 2.3) and which contains all nuclear vector spaces and all locally compact abelian groups. We prove in 5.6 that the Hausdorff variety generated by all nuclear vector spaces and all locally compact abelian groups (denoted by 𝒱₁) is strictly smaller than the Hausdorff variety of all nuclear groups (denoted by 𝒱₂). More precisely,...

Some geometrical properties of infinite-dimensional bilinear controlled systems

Naceurdine Bensalem, Fernand Pelletier (1999)

Banach Center Publications

The study of controlled infinite-dimensional systems gives rise to many papers (see for instance [GXL], [GXB], [X]) but it is also motivated by various mathematical problems: partial differential equations ([BP]), sub-Riemannian geometry on infinite-dimensional manifolds ([Gr]), deformations in loop-spaces ([AP], [PS]). The first difference between finite and infinite-dimensional cases is that solutions in general do not exist (even locally) for every given control function. The aim of this paper...

Currently displaying 81 – 100 of 324