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951.
《代数通讯》2013,41(8):2809-2825
Let k be a field and An(ω) be the Taft's n2-dimensional Hopf algebra. When n is odd, the Drinfeld quantum double D(An(ω)) of An(ω) is a ribbon Hopf algebra. In the previous articles, we constructed an n4-dimensional Hopf algebra Hn(p, q) which is isomorphic to D(An(ω)) if p ≠ 0 and q = ω?1 , and studied the irreducible representations of Hn(1, q) and the finite dimensional representations of H3(1, q). In this article, we examine the finite-dimensional representations of Hn(l q), equivalently, of D(An(ω)) for any n ≥ 2. We investigate the indecomposable left Hn(1, q)-module, and describe the structures and properties of all indecomposable modules and classify them when k is algebraically closed. We also give all almost split sequences in mod Hn(1, q), and the Auslander-Reiten-quiver of Hn(1 q). 相似文献
952.
953.
F. Sommen 《Applicable analysis》2013,92(1-2):225-253
In this paper we present some basic function theoretic results and ideas concerning nullsolutions of several Dirac type operators. In particular we consider plane wave solutions, axial symmetry, zonal functions and irreducible representations of the group SO (m). 相似文献
954.
955.
Rodica Curtu 《Physica D: Nonlinear Phenomena》2010,239(9):504-514
Recent studies of a firing rate model for neural competition as observed in binocular rivalry and central pattern generators [R. Curtu, A. Shpiro, N. Rubin, J. Rinzel, Mechanisms for frequency control in neuronal competition models, SIAM J. Appl. Dyn. Syst. 7 (2) (2008) 609-649] showed that the variation of the stimulus strength parameter can lead to rich and interesting dynamics. Several types of behavior were identified such as: fusion, equivalent to a steady state of identical activity levels for both neural units; oscillations due to either an escape or a release mechanism; and a winner-take-all state of bistability. The model consists of two neural populations interacting through reciprocal inhibition, each endowed with a slow negative-feedback process in the form of spike frequency adaptation. In this paper we report the occurrence of another complex oscillatory pattern, the mixed-mode oscillations (MMOs). They exist in the model at the transition between the relaxation oscillator dynamical regime and the winner-take-all regime. The system distinguishes itself from other neuronal models where MMOs were found by the following interesting feature: there is no autocatalysis involved (as in the examples of voltage-gated persistent inward currents and/or intrapopulation recurrent excitation) and therefore the two cells in the network are not intrinsic oscillators; the oscillations are instead a combined result of the mutual inhibition and the adaptation. We prove that the MMOs are due to a singular Hopf bifurcation point situated in close distance to the transition point to the winner-take-all case. We also show that in the vicinity of the singular Hopf other types of bifurcations exist and we construct numerically the corresponding diagrams. 相似文献
956.
The three integrable two-dimensional Hénon-Heiles systems and their integrable perturbations are revisited. A family of new integrable perturbations is found, and N-dimensional completely integrable generalizations of all these systems are constructed by making use of sl(2,R)⊕h3 as their underlying Poisson symmetry algebra. In general, the procedure here introduced can be applied in order to obtain N-dimensional integrable generalizations of any 2D integrable potential of the form , and the formalism gives the explicit form of all the integrals of the motion. Further applications of this algebraic approach in different contexts are suggested. 相似文献
957.
It has been shown by Albuquerque and Majid that a class of unital k-algebras, not necessarily associative, obtained through the Cayley–Dickson process can be viewed as commutative associative algebras in some suitable symmetric monoidal categories. In this note we will prove that they are, moreover, commutative and cocommutative weak braided Hopf algebras within these categories. To this end we first define a Cayley–Dickson process for coalgebras. We then see that the k-vector space of complex numbers, of quaternions, of octonions, of sedenions, etc. fit to our theory, hence they are all monoidal coalgebras as well, and therefore weak braided Hopf algebras. 相似文献
958.
We study several families of semisimple Hopf algebras, arising as bismash products, which are constructed from finite groups with a certain specified factorization. First we associate a bismash product Hq of dimension q(q−1)(q+1) to each of the finite groups PGL2(q) and show that these Hq do not have the structure (as algebras) of group algebras (except when q=2,3). As a corollary, all Hopf algebras constructed from them by a comultiplication twist also have this property and are thus non-trivial. We also show that bismash products constructed from Frobenius groups do have the structure (as algebras) of group algebras. 相似文献
959.
Let G be a unipotent algebraic subgroup of some defined over . We describe an algorithm for finding a finite set of generators of the subgroup . This is based on a new proof of the result (in more general form due to Borel and Harish-Chandra) that such a finite generating set exists. 相似文献
960.
In this paper, we consider the following delayed Leslie-Gower predator-prey system
(∗) 相似文献