Selecta Mathematica
1420-9020
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Các bài báo tiêu biểu
A tetrachotomy for expansions of the real ordered additive group
Tập 27 - Trang 1-36 - 2021
Let $$\mathcal {R}$$ be an expansion of the ordered real additive group. When
$$\mathcal {R}$$ is o-minimal, it is known that either $$\mathcal {R}$$ defines
an ordered field isomorphic to $$(\mathbb {R},<,+,\cdot )$$ on some open
subinterval $$I\subseteq \mathbb {R}$$ , or $$\mathcal {R}$$ is a reduct of an
ordered vector space. We say $$\mathcal {R}$$ is field-type if it satisfies the
former con...
Cohomology of semisimple local systems and the decomposition theorem
Tập 30 - Trang 1-62 - 2023
In this paper, we study the cohomology of semisimple local systems in the spirit
of classical Hodge theory. On the one hand, we construct a generalized Weil
operator from the complex conjugate of the cohomology of a semisimple local
system to the cohomology of its dual local system, which is functorial with
respect to smooth restrictions. This operator allows us to study the Poincaré
pairing, usua...
The universality of Hughes-free division rings
Tập 27 - Trang 1-33 - 2021
Let $$E*G$$ be a crossed product of a division ring E and a locally indicable
group G. Hughes showed that up to $$E*G$$ -isomorphism, there exists at most one
Hughes-free division $$E*G$$ -ring. However, the existence of a Hughes-free
division $$E*G$$ -ring $${\mathcal {D}}_{E*G}$$ for an arbitrary locally
indicable group G is still an open question. Nevertheless, $${\mathcal
{D}}_{E*G}$$ exists, ...
Computation of cohomology of Lie conformal and Poisson vertex algebras
Tập 26 - Trang 1-51 - 2020
We develop methods for computation of Poisson vertex algebra cohomology. This
cohomology is computed for the free bosonic and fermionic Poisson vertex
(super)algebras, as well as for the universal affine and Virasoro Poisson vertex
algebras. We establish finite dimensionality of this cohomology for conformal
Poisson vertex (super)algebras that are finitely and freely generated by
elements of posit...
Adjacency of Young tableaux and the Springer fibers
Tập 12 - Trang 517-540 - 2007
We connect different results about irreducible components of the Springer fibers
of type A. Firstly, we show a relation between the Spaltenstein partition of the
fibers and a total order $${\prec}$$ on the set of standard Young tableaux.
Next, using a result of Steinberg, we connect a work of the first author to the
Robinson–Schensted map. We also perform the Spaltenstein study of the relative
pos...
Pseudo-potentials, nonlocal symmetries and integrability of some shallow water equations
Tập 12 - Trang 241-270 - 2006
Zero curvature formulations, pseudo-potentials, modified versions, “Miura
transformations”, conservation laws, and nonlocal symmetries of the Korteweg–de
Vries, Camassa–Holm and Hunter–Saxton equations are investigated from a unified
point of view: these three equations belong to a two-parameter family of
equations describing pseudo-spherical surfaces, and therefore their basic
integrability prope...