1,247 research outputs found
Homomorphisms on infinite direct product algebras, especially Lie algebras
We study surjective homomorphisms f:\prod_I A_i\to B of
not-necessarily-associative algebras over a commutative ring k, for I a
generally infinite set; especially when k is a field and B is
countable-dimensional over k.
Our results have the following consequences when k is an infinite field, the
algebras are Lie algebras, and B is finite-dimensional:
If all the Lie algebras A_i are solvable, then so is B.
If all the Lie algebras A_i are nilpotent, then so is B.
If k is not of characteristic 2 or 3, and all the Lie algebras A_i are
finite-dimensional and are direct products of simple algebras, then (i) so is
B, (ii) f splits, and (iii) under a weak cardinality bound on I, f is
continuous in the pro-discrete topology. A key fact used in getting (i)-(iii)
is that over any such field, every finite-dimensional simple Lie algebra L can
be written L=[x_1,L]+[x_2,L] for some x_1, x_2\in L, which we prove from a
recent result of J.M.Bois.
The general technique of the paper involves studying conditions under which a
homomorphism on \prod_I A_i must factor through the direct product of finitely
many ultraproducts of the A_i.
Several examples are given, and open questions noted.Comment: 33 pages. The lemma in section 12.1 of the previous version was
incorrect, and has been removed. (Nothing else depended on it.) Other changes
are improvements in wording, et
The Doxastic Interpretation of Team Semantics
We advance a doxastic interpretation for many of the logical connectives
considered in Dependence Logic and in its extensions, and we argue that Team
Semantics is a natural framework for reasoning about beliefs and belief
updates
Symmetrization in Geometry
The concept of an -symmetrization is introduced, which provides a
convenient framework for most of the familiar symmetrization processes on
convex sets. Various properties of -symmetrizations are introduced and the
relations between them investigated. New expressions are provided for the
Steiner and Minkowski symmetrals of a compact convex set which exhibit a dual
relationship between them. Characterizations of Steiner, Minkowski and central
symmetrization, in terms of natural properties that they enjoy, are given and
examples are provided to show that none of the assumptions made can be dropped
or significantly weakened. Other familiar symmetrizations, such as Schwarz
symmetrization, are discussed and several new ones introduced.Comment: A chacterization of central symmetrization has been added and several
typos have been corrected. This version has been accepted for publication on
Advances in Mathematic
Generating perfect fluid spheres in general relativity
Ever since Karl Schwarzschild's 1916 discovery of the spacetime geometry
describing the interior of a particular idealized general relativistic star --
a static spherically symmetric blob of fluid with position-independent density
-- the general relativity community has continued to devote considerable time
and energy to understanding the general-relativistic static perfect fluid
sphere. Over the last 90 years a tangle of specific perfect fluid spheres has
been discovered, with most of these specific examples seemingly independent
from each other. To bring some order to this collection, in this article we
develop several new transformation theorems that map perfect fluid spheres into
perfect fluid spheres. These transformation theorems sometimes lead to
unexpected connections between previously known perfect fluid spheres,
sometimes lead to new previously unknown perfect fluid spheres, and in general
can be used to develop a systematic way of classifying the set of all perfect
fluid spheres.Comment: 18 pages, 4 tables, 4 figure
Cognitive constraints, contraction consistency, and the satisficing criterion
© 2007, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0
EF+EX Forest Algebras
We examine languages of unranked forests definable using the temporal
operators EF and EX. We characterize the languages definable in this logic, and
various fragments thereof, using the syntactic forest algebras introduced by
Bojanczyk and Walukiewicz. Our algebraic characterizations yield efficient
algorithms for deciding when a given language of forests is definable in this
logic. The proofs are based on understanding the wreath product closures of a
few small algebras, for which we introduce a general ideal theory for forest
algebras. This combines ideas from the work of Bojanczyk and Walukiewicz for
the analogous logics on binary trees and from early work of Stiffler on wreath
product of finite semigroups
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