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1.
A. G. Pinus 《Algebra and Logic》1998,37(4):245-259
We construct a conditional identity calculus (similar to the Birkhoff identity calculus), which complies with the concept
of truth for a conditional identity on a universal algebra. The relationship is studied between the isomorphism of embedding
categories of conditional varieties and the conditioned rational equivalence of these varieties. As applications, we describe
invariants for the relations ‘is conditional rational equivalent’ and ‘is similar’ on finite universal algebras.
Supported by RFFR grant No. 93-01-01520.
Translated fromAlgebra i Logika, Vol. 37, No. 4, pp. 432–459, July–August, 1998. 相似文献
2.
Mićo Durdević 《Israel Journal of Mathematics》1997,98(1):329-348
A generalization of Hopf algebras (quantum groups), and braided-Hopf algebras (braided quantum groups) in which the multiplicativity
axiom for the counit is dropped, is presented. The generalization overcomes an inherent geometrical inhomogeneity of standard
quantum groups and braided quantum groups, in the sense of allowing completely ‘pointless’ objects. All braid-type equations
appear as a consequence of deeper axioms. Braided counterparts of basic algebraic relations between fundamental entities of
the standard theory are found. 相似文献
3.
We characterize hereditary (as coalgebras) Hopf algebras by the property of ‘equivariant smoothness’, and apply the result
to generalize to the super-context, the category equivalence, due to Hochschild, between the unipotent algebraic affine groups
and the finite-dimensional nilpotent Lie algebras, in characteristic zero. The global dimension of commutative Hopf algebras,
regarded as coalgebras, is also discussed.
Presented by S. Montgomery
Mathematics Subject Classification (2000) 16W30. 相似文献
4.
Jean-Marie Bois 《Mathematische Zeitschrift》2009,262(4):715-741
In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the ‘one and a half generation’ property,
i.e. when every non-zero element can be completed to a generating pair. We show that classical simple algebras have this property,
and that the only simple Cartan type algebras of type W which have this property are the Zassenhaus algebras.
The author was partially supported by the European Community’s Human Potential Programme under contract HPRN-CT-2002-00287
(RTN Network “K-Theory, Algebraic Groups and Related Structures”) and a long-term research grant from the D.A.A.D. 相似文献
5.
Birkhoff Completeness in Institutions 总被引:1,自引:0,他引:1
We develop an abstract proof calculus for logics whose sentences are ‘Horn sentences’ of the form: and prove an institutional generalization of Birkhoff completeness theorem. This result is then applied to the particular
cases of Horn clauses logic, the ‘Horn fragment’ of preorder algebras, order-sorted algebras and partial algebras and their
infinitary variants.
the restriction of a logic to Horn sentences 相似文献
6.
A previously proposed algebra of asymptotic fields in quantum electrodynamics is formulated as a net of algebras localized
in regions which in general have unbounded spacelike extension. Electromagnetic fields may be localized in ‘symmetrical spacelike
cones’, but there are strong indications this is not possible in the present model for charged fields, which have tails extending
in all space directions. Nevertheless, products of appropriately ‘dressed’ fermion fields (with compensating charges) yield
bi-localized observables. 相似文献
7.
I. Grattan-Guinness 《Logica Universalis》2011,5(1):21-73
A prized property of theories of all kinds is that of generality, of applicability or least relevance to a wide range of circumstances and situations. The purpose of this article is to present
a pair of distinctions that suggest that three kinds of generality are to be found in mathematics and logics, not only at
some particular period but especially in developments that take place over time: ‘omnipresent’ and ‘multipresent’ theories,
and ‘ubiquitous’ notions that form dependent parts, or moments, of theories. The category of ‘facets’ is also introduced,
primarily to assess the roles of diagrams and notations in these two disciplines. Various consequences are explored, starting
with means of developing applied mathematics, and then reconsidering several established ways of elaborating or appraising
theories, such as analogising, revolutions, abstraction, unification, reduction and axiomatisation. The influence of theories
already in place upon theory-building is emphasised. The roles in both mathematics and logics of set theory, abstract algebras,
metamathematics, and model theory are assessed, along with the different relationships between the two disciplines adopted
in algebraic logic and in mathematical logic. Finally, the issue of monism versus pluralism in these two disciplines is rehearsed,
and some suggestions are made about the special character of mathematical and logical knowledge, and also the differences
between them. Since the article is basically an exercise in historiography, historical examples and case studies are described
or noted throughout. 相似文献
8.
Christopher Hollings 《Semigroup Forum》2010,80(3):453-476
We extend the ‘∨-premorphisms’ part of the Ehresmann-Schein-Nambooripad Theorem to the case of two-sided restriction semigroups and inductive
categories, following on from a result of Lawson (J. Algebra 141:422–462, 1991) for the ‘morphisms’ part. However, it is so-called ‘∧-premorphisms’ which have proved useful in recent years in the study of partial actions. We therefore obtain an Ehresmann-Schein-Nambooripad-type
theorem for (ordered) ∧-premorphisms in the case of two-sided restriction semigroups and inductive categories. As a corollary, we obtain such a theorem
in the inverse case. 相似文献
9.
In this paper, a simple probabilistic model of coalition formation provides a unified interpretation for several extensions
of the Shapley value. Weighted Shapley values, semivalues, weak (weighted or not) semivalues, and the Shapley value itself
appear as variations of this model. Moreover, some notions that have been introduced in the search of alternatives to Shapley’s
seminal characterization, as ‘balanced contributions’ and the ‘potential’ are reinterpreted from this point of view. Natural
relationships of these conditions with some mentioned families of ‘values’ are shown. These reinterpretations strongly suggest
that these conditions are more naturally interpreted in terms of coalition formation than in terms of the classical notion
of ‘value.’
相似文献
10.
We construct irreducible representations of affine Khovanov–Lauda–Rouquier algebras of arbitrary finite type. The irreducible
representations arise as simple heads of appropriate induced modules, and thus our construction is similar to that of Bernstein
and Zelevinsky for affine Hecke algebras of type A. The highest weights of irreducible modules are given by the so-called good words, and the highest weights of the ‘cuspidal
modules’ are given by the good Lyndon words. In a sense, this has been predicted by Leclerc. 相似文献
11.
We study pro-‘finite dimensional finite exponent’ completions of restricted Lie algebras over finite fields of characteristicp. These compact Hausdorff topological restricted Lie algebras, called pro-
restricted Lie algebras, are the restricted Lie-theoretic analogues of pro-p groups. A structure theory for pro-
restricted Lie algebras with finite rank is developed. In particular, the centre of such a Lie algebra is shown to be open.
As an application we examinep-adic analytic pro-p groups in terms of their associated pro-
restricted Lie algebras.
Supported by NSERC of Canada. 相似文献
12.
Classical composition algebras, with a unit element, are well-known and can be obtained by means of the Cayley-Dickson doubling
process. If the condition on the existence of unit element is dropped, many new algebras arise. However, it is shown in this
paper that if such a weak condition as the associativity of third powers of any element is imposed, only the known flexible
composition algebras appear.
Partially supported by the DGICYT (PS 90-0129) and by the DGA (PCB-6/91)
Supported by a grant from the ‘Plan de Formación del Personal Investigador’ (DGICYT, Spain)
This article was processed by the authors using the Springer-Verlag TEX P Jour1g macro package 1991. 相似文献
13.
Elisabeth Schellekens 《Acta Analytica》2005,20(4):10-23
The principal concern of my paper is a distinction between two ways of appreciating works of art, characterised here in terms
of the phrases ‘seeing is believing’ and ‘believing is seeing’. I examine this distinction in the light of an epistemological
requirement at times at least grounded in what David Davies, in his Art as Performance, refers to as the ‘common sense theory of art appreciation’ in order to assess exactly what aspect of the philosophical approach
generally known as aesthetic empiricism his account commits him to reject. I argue that the ‘experiential requirement’, if
only conceived in a slightly broader way than is usual, might very well have an important role to play not only in the appropriate
appreciation of works that do not demonstrate the need for such a requirement (primarily works of late modern and conceptual
art), but also in the ontological account Davies himself favours. 相似文献
14.
Andrew Nicas 《K-Theory》2005,35(3-4):273-339
Traces taking values in suitable ‘Hochschild complexes’ are defined in the context of symmetric monoidal categories and applied
to various categories of chain complexes, simplicial abelian groups, and symmetric spectra. Topological applications to parametrized
fixed point theory are given.
(Received: October 2003)
Partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada. 相似文献
15.
Constellations were recently introduced by the authors as one-sided analogues of categories: a constellation is equipped with a partial
multiplication for which ‘domains’ are defined but, in general, ‘ranges’ are not. Left restriction semigroups are the algebraic objects modelling semigroups of partial mappings, equipped with local identities in the domains of the
mappings. Inductive constellations correspond to left restriction semigroups in a manner analogous to the correspondence between inverse semigroups and inductive
groupoids. 相似文献
16.
D. Neuenschwander 《Journal of Mathematical Sciences》1997,84(3):1138-1144
Carrying over a result of Kuelbs and Ledoux, we show that in generalized convolution algebras as introduced by Urbanik, domains
of attraction of stable measures go over, after suitable truncation and renormalization, into domains of attraction of the
characteristic measure of the convolution algebra. For convolutions which are induced by a (deterministic) semigroup operation,
only the “large” terms are responsible for convergence to the stable law.
Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part III 相似文献
17.
H. Vernaeve 《Monatshefte für Mathematik》2003,80(2):307-318
It is a known open question whether in Rosinger’s nowhere dense quotient algebra distributions can be embedded, ensuring consistency with partial derivatives. In this paper, we construct algebras of generalized functions with nowhere dense singularities similar to Rosinger’s algebra in which such an embedding of distributions is possible. Moreover, in some of the algebras, the embedding preserves the products of smooth functions. Further, we indicate that most of the properties of Rosinger’s algebra, in particular concerning the solvability of nonlinear PDEs, remain valid in the new algebras. Summarizing, we give a positive answer to the above-mentioned open question, if one allows a modification in the definition of the algebra that does not affect its basic properties. 相似文献
18.
C. J. van Alten 《Algebra Universalis》2009,62(4):419-451
A residuated ordered algebra is a partially ordered set with additional ‘residuated’ operations. A construction is presented
that, from any partial subalgebra of a residuated ordered algebra, constructs a complete algebra into which the partial subalgebra
embeds. Conditions are given under which the constructed algebra is finite whenever a finite partial subalgebra is chosen.
This implies the ‘finite embeddability property’ for the given class of residuated ordered algebras. In the case that the
whole algebra is chosen as the partial subalgebra, the construction is a completion of the underlying order of the algebra.
A scheme of inequalities is described that are shown to have the property of being preserved by the above construction. These
preservation results thus extend the results on the finite embeddability property and completion. 相似文献
19.
H. Vernaeve 《Monatshefte für Mathematik》2003,138(4):307-318
It is a known open question whether in Rosinger’s nowhere dense quotient algebra distributions can be embedded, ensuring
consistency with partial derivatives. In this paper, we construct algebras of generalized functions with nowhere dense singularities
similar to Rosinger’s algebra in which such an embedding of distributions is possible. Moreover, in some of the algebras,
the embedding preserves the products of smooth functions. Further, we indicate that most of the properties of Rosinger’s algebra,
in particular concerning the solvability of nonlinear PDEs, remain valid in the new algebras. Summarizing, we give a positive
answer to the above-mentioned open question, if one allows a modification in the definition of the algebra that does not affect
its basic properties.
Received September 20, 2001; in final form April 11, 2002 相似文献
20.
We transfer a large part of the circle of theorems characterizing the generalization of classical H∞ known as ‘weak* Dirichlet algebras’, to Arveson’s very general noncommutative setting of subalgebras of finite von Neumann
algebras. This solves the long-standing open question of the equivalence of principles such as Szeg?’s theorem, the weak*
density of A + A*, and so on, within the noncommutative setting. The techniques should also be useful in future developments in noncommutative
Hp theory. 相似文献