On pointed Hopf algebras associated with alternating and dihedral groups

We classify finite-dimensional complex pointed Hopf algebra with group of group-like elements isomorphic to A_5. We show that any pointed Hopf algebra with infinitesimal braiding associated with the conjugacy class of $\pi$ \in $A_n$ is infinite-dimensional if the order of $\pi$ is odd except for $\pi=(1 2 3)$ in $A_4$. We also study pointed Hopf algebras over the dihedral groups.Comment: v2: minor corrections, we remove Table 1 and change Remark 3.4; v3: minor corrections, we modify reference [FGV]; final version to appear in Rev. Uni\'on Mat. Argent., 17 page

On pointed Hopf algebras over dihedral groups

Let k be an algebraically closed field of characteristic 0 and let D_m be the dihedral group of order 2m with m= 4t, with t bigger than 2. We classify all finite-dimensional Nichols algebras over D_m and all finite-dimensional pointed Hopf algebras whose group of group-likes is D_m, by means of the lifting method. Our main result gives an infinite family of non-abelian groups where the classification of finite-dimensional pointed Hopf algebras is completed. Moreover, it provides for each dihedral group infinitely many non-trivial new examples.Comment: 23 pages, 1 figure and several table

On pointed Hopf algebras associated to unmixed conjugacy classes in S_n

Let s in S_n be a product of disjoint cycles of the same length, C the conjugacy class of s and rho an irreducible representation of the isotropy group of s. We prove that either the Nichols algebra B(C, rho) is infinite-dimensional, or the braiding of the Yetter-Drinfeld module is negative

Conjugacy classes of p-cycles of type D in alternating groups

We classify the conjugacy classes of p-cycles of type D in alternating groups. This finishes the open cases in arXiv:0812.4628. We also determine all the subracks of those conjugacy classes which are not of type D.Comment: Second paragraph of subsection 2.2 rewritten. 4-th sentence of subsection 2.4 rewritten. More explanations added in Remark 2.4. Lemma 2.5 and Corollary 2.7 added. Appendix removed and put it as Remark 3.1. Remark 3.2 (former 3.1) reorganized. References: [Da], [EGSS], [H], [IS] added, [GPPS] removed. Communications in Algebra (2014

A novel trajectory concept for a mission to the Inner Large Moons of Saturn

We present a novel concept for a small mission to the four inner large satellites of Saturn. Leveraging the high efficiency of electric propulsion, the concept enables orbit insertion around each of the moons, for arbitrarily long close observation periods. The mission starts with a EVVES interplanetary segment, where a combination of multiple gravity assist and deep space low thrust enables reduced relative arrival velocity at Saturn. As a result, an unpowered capture via a sequence of resonant flybys with Titan is possible. The transfers between moons use a low-thrust control law that connects unstable and stable branches of the invariant manifolds of planar Lyapunov orbits from the circular restricted three-body problem of each moon and Saturn. The exploration of the moons relies on homoclinic and heteroclinic connections of the Lyapunov orbits around the L$_1$ and L$_2$ equilibrium points. These science orbits can be extended for arbitrary lengths of time with negligible propellant usage. The strategy enables a comprehensive scientific exploration of the inner large moons, located deep inside the gravitational well of Saturn, which is unfeasible with conventional impulsive maneuvers due to excessive fuel consumption

Algebras de Hopf punteadas sobre grupos no abelianos /

Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física, 2008.Sea G un grupo finito no abeliano. Esta tesis trata acerca del problema de clasificación de las álgebras de Hopf punteadas complejas de dimensión finita H con grupo de elementos de tipo grupo G(H) isomorfo a G. Se analizan criterios que permiten dar condiciones suficientes para que el álgebra de Nichols B(O,f) tenga dimensión infinita estudiando subracks de O, donde O es una clase de conjugación de G y f es una representación irreducible de G^s, el centralizador de un elemento fijo s en O.Fernando Amado Fantino ; director Nicolás Andruskiewitsch