共查询到20条相似文献,搜索用时 93 毫秒
1.
We study Basic algebra, the algebraic structure associated with basic propositional calculus, and some of its natural extensions. Among other things, we prove the amalgamation property for the class of Basic algebras, faithful Basic algebras and linear faithful Basic algebras. We also show that a faithful theory has the interpolation property if and only if its correspondence class of algebras has the amalgamation property. 相似文献
2.
In this paper, we define a class of extended quantum enveloping algebras U q (f(K, J)) and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction generalizes some well-known extensions of quantum enveloping algebras by a Hopf algebra and provides a large of new noncommutative and noncocommutative Hopf algebras. 相似文献
3.
Hannes Pouseele 《Geometriae Dedicata》2006,122(1):77-88
We discuss three general problems concerning the cohomology of a (real or complex) nilpotent Lie algebra: first of all, determining
the Betti numbers exactly; second, determining the distribution these Betti numbers follow; and finally, estimating the size
of the individual cohomology spaces or the total cohomology space. We show how spectral sequence arguments can contribute
to a solution in a concrete setting. For one-dimensional extensions of a Heisenberg algebra, we determine the Betti numbers
exactly. We then show that some families in this class have a M-shaped Betti number distribution, and construct the first
examples with an even more exotic Betti number distribution. Finally, we discuss the construction of (co)homology classes
for split metabelian Lie algebras, thus proving the Toral Rank Conjecture for this class of algebras. 相似文献
4.
5.
6.
In this paper,we will give the definition of completable nilpotent Lie algebras,discuss its decomposition and prove that the heisenberg algebras and extensions of abelian quadratic Lie algebras are all completable nilpotent Lie algebras. 相似文献
7.
Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure
theory (such as (co)homology groups, universal central extensions) of Hom-Leibniz algebras based on some works of Loday and
Pirashvili. 相似文献
8.
In this note we give an interpretation of cylindric algebras as algebras of sentences (rather than formulas) of first order logic. We show that the isomorphism types of such algebras of sentences coincide with the class of neat reducts of cylindric algebras. Also we show how this interpretation sheds light on some recent results. This is done by likening Henkin's Neat Embedding Theorem to his celebrated completeness proof. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
9.
10.
In this article, we commence to study the real (simple) left-symmetric algebras. From the known classification of certain complex (semi)simple left-symmetric algebras, we classify their corresponding real forms. We not only obtain the classification of real simple left-symmetric algebras in low dimensions, but also find certain examples of real simple left-symmetric algebras in higher dimensions. In particular, there exists a complex simple left-symmetric algebra without any real form. We also give a geometric construction for a class of real simple left-symmetric algebras. At last, we apply the classification results to study some structures related to geometry. 相似文献
11.
A. P. Pozhidaev 《Siberian Mathematical Journal》2008,49(4):696-708
We consider some algebraical systems that lead to various nearly associative triple systems. We deal with a class of algebras which contains Leibniz-Poisson algebras, dialgebras, conformal algebras, and some triple systems. We describe all homogeneous structures of ternary Leibniz algebras on a dialgebra. For this purpose, in particular, we use the Leibniz-Poisson structure on a dialgebra. We then find a corollary describing the structure of a Lie triple system on an arbitrary dialgebra, a conformal associative algebra and a classical associative triple system. We also describe all homogeneous structures of an (ε, δ)-Freudenthal-Kantor triple system on a dialgebra. 相似文献
12.
We study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finite-dimensional algebras, we develop our results first in that general setting, and then specialize to the above situations. From this we obtain new proofs of several known results in modular representation theory of symmetric groups. Moreover, we reduce certain questions about computing extensions for symmetric groups and Hecke algebras to questions about extensions for general linear groups and their quantizations. 相似文献
13.
The goal of this article is to generalize the theory of Hopf–Ore extensions on Hopf algebras to multiplier Hopf algebras. First the concept of a Hopf–Ore extension of a multiplier Hopf algebra is introduced. We give a necessary and sufficient condition for Ore extensions to become a multiplier Hopf algebra. Finally, *-structures are constructed on Hopf–Ore extensions, and certain isomorphisms between Hopf–Ore extensions are discussed. 相似文献
14.
In this article we study the problem when a left distributive algebra over a field determines an atom of the lattice of all radicals of rings. We show that this problem is strictly connected with the problem of describing extensions of left chain algebras and give a characterization of left chain algebras determining atoms. 相似文献
15.
M. Schocker 《Journal of Algebraic Combinatorics》2008,28(1):231-234
We define the notion of weakly ordered semigroups. For this class of semigroups, we compute the radical of the semigroup algebras.
This generalizes some results on left regular bands and on 0- Hecke algebras. 相似文献
16.
We study Dorroh extensions of algebras and Dorroh extensions of coalgebras. Their structures are described. Some properties of these extensions are presented. We also introduce the finite duals of algebras and modules which are not necessarily unital. Using these finite duals, we determine the dual relations between the two kinds of extensions. 相似文献
17.
Given a generalized Weyl algebra A of degree 1 with the base algebra D, we prove that the difference of the Gelfand–Kirillov dimension of A and that of D could be any positive integer or infinity. Under mild conditions, this difference is exactly 1. As applications, we calculate the Gelfand–Kirillov dimensions of various algebras of interest, including the (quantized) Weyl algebras, ambiskew polynomial rings, noetherian (generalized) down-up algebras, iterated Ore extensions, quantum Heisenberg algebras, universal enveloping algebras of Lie algebras, quantum GWAs, etc. 相似文献
18.
Towards a Lie theory of locally convex groups 总被引:3,自引:0,他引:3
Karl-Hermann Neeb 《Japanese Journal of Mathematics》2006,1(2):291-468
In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled
on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie subgroups, and integrability
of Lie algebra extensions to Lie group extensions. We further describe how regularity or local exponentiality of a Lie group
can be used to obtain quite satisfactory answers to some of the fundamental problems. These results are illustrated by specialization
to some specific classes of Lie groups, such as direct limit groups, linear Lie groups, groups of smooth maps and groups of
diffeomorphisms. 相似文献
19.
20.
引入一个具有Heyting结构Ockham代数,简称HO-代数.所谓HO-代数,是指具有(2,2,2,1,0,0)类型的代数(L;∧,∨,→,f,0,1).其中(L;f)是Ockham代数,(L;→)是Heyting代数,且运算f和→由恒等式f(x→y)=f^2(x)∧f(y)与f(x)→y=f^2(x)∨y所连结.主要讨论了HO-代数的同余关系的性质.并刻画了其次直不可约代数的某些性质. 相似文献