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41.
Leibniz agebras are a generalization of Lie algebras, where no symmetry properties of the bracket are required. In this Letter we introduce a notion of R-matrices for this structure and the related Yang–Baxter equations, and discuss some of their basic properties. 相似文献
42.
Vern I. Paulsen Dinesh Singh 《Proceedings of the American Mathematical Society》2004,132(12):3577-3579
We prove a uniform algebra analogue of a classical inequality of Bohr's concerning Fourier coefficients of bounded holomorphic functions. The classical inequality follows trivially.
43.
A. N. Koryukin 《Algebra and Logic》2003,42(6):387-397
We generalize a well-known two-parameter quantization for the group GL
2(k) (over an arbitrary field k). Specifically, a certain class of Hopf algebras is constructed containing that quantization. The algebras are constructed given an arbitrary coalgebra and an arbitrary pair of its commuting anti-isomorphisms, and are defined by quadratic relations. They are densely linked to the compact quantum groups introduced by Woronowicz. We give examples of Hopf algebras that can be rowed up to the two-parameter quantization for GL
2(k). 相似文献
44.
Kazumi Tsukada 《Geometriae Dedicata》1997,68(1):61-71
We investigate holomorphic maps between compact generalized Hopf manifolds (i.e., locally conformal Kähler manifolds with parallel Lee form). We show that they preserve the canonical foliations. Moreover, we study compact complex submanifolds of g.H. manifolds and holomorphic submersions from compact g.H. manifolds. 相似文献
45.
Simple modules over the Leibniz pairs are studied. Simple Poisson modules over Poisson algebras of the semisimple associative algebra structure are determined and they are nothing but simple bimodules over simple associative algebras with standard noncommutative Poisson algebra structure. 相似文献
46.
ON THE COHOMOLOGY OF GENERALIZED RESTRICTED LIE ALGEBRAS 总被引:2,自引:0,他引:2
Shu Bin 《数学年刊B辑(英文版)》1998,19(4):421-432
0.IntroductionThispaperisaimedatdevelopingthecohomologytheoryofmodularLiealgebrasandthendeterminingthefirstcohomologygroupsofCartantypeLiealgebras.AsgeneralizationoftheconceptofrestrictedLiealgebras,ageneralizedrestrictedLiealgebra(GRLiealgebra)wasintroducedin[21],whichisassociatedwithabasisandamappingofthebasisintotheLiealgebrasatisfyingthegeneralized-restrictednessconditions.Generalizedrestrictedrepresentations(GRrepresentations)werethenintroduced,whichcanbereducedtotherepresentationsofa… 相似文献
47.
We investigate certain classes of normal completely positive (CP) maps on the hyperfinite II1 factorA. Using the representation theory of a suitable irrational rotation algebra, we propose some computable invariants for such
CP maps.
Dedicated to Professor K B Sinha 相似文献
48.
Hopf Modules and Noncommutative Differential Geometry 总被引:1,自引:0,他引:1
We define a new algebra of noncommutative differential forms for any Hopf algebra with an invertible antipode. We prove that there is a one-to-one correspondence between anti-Yetter–Drinfeld modules, which serve as coefficients for the Hopf cyclic (co)homology, and modules which admit a flat connection with respect to our differential calculus. Thus, we show that these coefficient modules can be regarded as “flat bundles” in the sense of Connes’ noncommutative differential geometry. 相似文献
49.
The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two and three we give explicit formulas. 相似文献
50.
In this paper, we study the existence of periodic orbits bifurcating from stationary solutions of a planar dynamical system
of Filippov type. This phenomenon is interpreted as a generalized Hopf bifurcation. In the case of smoothness, Hopf bifurcation
is characterized by a pair of complex conjugate eigenvalues crossing through the imaginary axis. This method does not carry
over to nonsmooth systems, due to the lack of linearization at the origin which is located on the line of discontinuity. In
fact, generalized Hopf bifurcation is determined by interactions between the discontinuity of the system and the eigen-structures
of all subsystems. With the help of geometrical observations for a corresponding piecewise linear system, we derive an analytical
method to investigate the existence of periodic orbits that are
obtained by searching for the fixed points of return maps. 相似文献