The map of the Brauer group of a real algebraic surface to the invariant part of the Brauer group of its complexification
is studied. In this study, the real cycle map of the Picard group is used.
Translated fromMatematicheskie Zametki, Vol. 67, No. 2, pp. 211–220, February, 2000. 相似文献
Relations between the measurability and continuity of algebraic automorphisms of topological groups depending on the types
of groups are examined. Various cases are considered and theorems on the continuity of measurable automorphisms are proved;
for instance, such theorems are proved for separable locally compact groups and automorphisms measurable with respect to nonnegative
Haar measures. On the other hand, examples of nonmetrizable nonseparable compact groups with Haar measures and of non-locally-compact
separable metrizable groups with measures μ quasi-invariant with respect to dense subgroups admittings μ-measurable discontinous
automorphisms are given.
Translated fromMatenmaticheskie Zametki, Vol. 68, No. 1, pp. 105–112, July, 2000.
An erratum to this article can be found online at . 相似文献
The Brauer group of a noncomplete real algebraic surface is calculated. The calculations make use of equivariant cohomology.
The resulting formula is similar to the formula for a complete surface, but the proof is substantially different.
Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 355–359, March, 2000. 相似文献
By a theorem of L. Rédei if a finite abelian group is a direct product of its subsets such that each subset has a prime number of elements and contains the identity element of the group, then at least one of the factors must be a subgroup. The content of this paper is that this result holds for certain infinite abelian groups, too. Namely, for groups that are direct products of finitely many Prüferian groups and finite cyclic groups of prime power order, belonging to pairwise distinct primes. 相似文献
Using ideas of our recent work on automorphisms of residually nilpotent relatively free groups, we introduce a new growth function for subgroups of the automorphism groups of relatively free algebras Fn(V) over a field of characteristic zero and the related notion of Gelfand-Kirillov dimension, and study their behavior. We prove that, under some natural restrictions, the Gelfand-Kirillov dimension of the group of tame automorphisms of Fn(V) is equal to the Gelfand-Kirillov dimension of the algebra Fn(V). We show that, in some cases, the Gelfand-Kirillov dimension of the group of tame automorphisms of Fn(V) is smaller than the Gelfand-Kirillov dimension of the whole automorphism group, and calculate the Gelfand-Kirillov dimension of the automorphism group of Fn(V) for some important varieties V.Partially supported by Grant MM605/96 of the Bulgarian Foundation for Scientific Research.2000 Mathematics Subject Classification: primary 16R10, 16P90; secondary 16W20, 17B01, 17B30, 17B40 相似文献
A lacuna of a linear hyperbolic differential operator is a domain inside its propagation cone where a proper fundamental solution vanishes identically. Huygens' principle for the classical wave equation is the simplest important example of such a phenomenon. The study of lacunas for hyperbolic equations of arbitrary order was initiated by I. G. Petrovsky (1945). Extending and clarifying his results, Atiyah, Bott and Gårding (1970-73) developed a profound and complete theory for hyperbolic operators with constant coefficients. In contrast, much less is known about lacunas for operators with variable coefficients. In the present paper we study this problem for one remarkable class of partial differential operators with singular coefficients. These operators stem from the theory of special functions in several variables related to finite root systems (Coxeter groups). The underlying algebraic structure makes it possible to extend many results of the Atiyah-Bott-Gårding theory. We give a generalization of the classical Herglotz-Petrovsky-Leray formulas expressing the fundamental solution in terms of Abelian integrals over properly constructed cycles in complex projective space. Such a representation allows us to employ the Petrovsky topological condition for testing regular (strong) lacunas for the operators under consideration. Some illustrative examples are constructed. A relation between the theory of lacunas and the problem of classification of commutative rings of partial differential operators is discussed.
We study the second bounded cohomology of an amalgamated free product of groups, and an HNN extension of a group. As an application, we show that a group with infinitely many ends has infinite dimensional second bounded cohomology.