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F. Fantino

Publications and source records attributed to F. Fantino.

11 recordsLinked to original sources
arXiv2021

Review of the Classification and Properties of 40 Variable Stars in Sagittarius

This study aims to assess the properties and classification of 40 variable stars in Sagittarius, little studied since their discovery and reported in the Information Bulletin on Variable Stars (IBVS) 985 and update. Using data from previous studies and several astronomical databases, we performed our analysis mainly utilizing a period analysis software and comparing the photometric characteristics of the variables in a Colour-Absolute Magnitude Diagram. For all stars, the variability is confirmed. We discovered new significant results for the period and/or type of 15 variables and highlighted incorrect cross-reference names on astronomical databases for 5 stars. This assessment also identifies 9 cases for which results from the ASAS-SN Catalog of Variable Stars are systematically not consistent with the original light curves. A correct identification of NSV 10522 is provided.

astro-ph.SR↗
arXiv2012

On twisted conjugacy classes of type D in sporadic simple groups

We classify twisted conjugacy classes of type D associated to the sporadic simple groups. This is an important step in the program of the classification of finite-dimensional pointed Hopf algebras with non-abelian coradical. As a by-product we prove that every complex finite-dimensional pointed Hopf algebra over the group of automorphisms of M12, J2, Suz, He, HN, T is the group algebra. In the appendix we improve the study of conjugacy classes of type D in sporadic simple groups.

math.QA↗
arXiv2010

Pointed Hopf algebras over the sporadic simple groups

We show that every finite-dimensional complex pointed Hopf algebra with group of group-likes isomorphic to a sporadic group is a group algebra, except for the Fischer group Fi22, the Baby Monster and the Monster. For these three groups, we give a short list of irreducible Yetter-Drinfeld modules whose Nichols algebra is not known to be finite-dimensional.

math.QA↗
arXiv2010

On Nichols algebras associated to simple racks

This is a report on the present state of the problem of determining the dimension of the Nichols algebra associated to a rack and a cocycle. This is relevant for the classification of finite-dimensional complex pointed Hopf algebras whose group of group-likes is non-abelian. We deal mainly with simple racks. We recall the notion of rack of type D, collect the known lists of simple racks of type D and include preliminary results for the open cases. This notion is important because the Nichols algebra associated to a rack of type D and any cocycle has infinite dimension. For those racks not of type D, the computation of the cohomology groups is needed. We discuss some techniques for this problem and compute explicitly the cohomology groups corresponding to some conjugacy classes in symmetric or alternating groups of low order.

math.QA↗
arXiv2010

On Twisted homogeneous racks of type D

We develop some techniques to check when a twisted homogeneous rack of class (L,t,θ) is of type D. Then we apply the obtained results to the cases L an alternating group on n letters, n\geq 5, or L a sporadic group.

math.QA↗
arXiv2010

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.

math.QA↗
arXiv2010

On pointed Hopf algebras associated with the symmetric groups II

This is a sequel to arXiv:0807.2406. It is shown that the Nichols algebras over the symmetric groups S_m, m > 4, are all infinite-dimensional, except (maybe) those related to the transpositions considered by Fomin and Kirillov, resp. Milinski and Schneider, and the class of type (2,3) in S_5.

math.QA↗
arXiv2010

Pointed Hopf algebras over some sporadic simple groups

Any finite-dimensional complex pointed Hopf algebra with group of group-likes isomorphic to a sporadic group, with the possible exception of the Fischer groups Fi22, the Baby Monster B and the Monster M, is a group algebra.

math.QA↗
arXiv2010

Finite-dimensional pointed Hopf algebras with alternating groups are trivial

It is shown that Nichols algebras over alternating groups A_m, m>4, are infinite dimensional. This proves that any complex finite dimensional pointed Hopf algebra with group of group-likes isomorphic to A_m is isomorphic to the group algebra. In a similar fashion, it is shown that the Nichols algebras over the symmetric groups S_m are all infinite-dimensional, except maybe those related to the transpositions considered in [FK], and the class of type (2,3) in S_5. We also show that any simple rack X arising from a symmetric group, with the exception of a small list, collapse, in the sense that the Nichols algebra of (X,q) is infinite dimensional, for q an arbitrary cocycle. arXiv:0904.3978 is included here.

math.QA↗
arXiv2008

New techniques for pointed Hopf algebras

We present techniques that allow to decide that the dimension of some pointed Hopf algebras associated with non-abelian groups is infinite. These results are consequences of arXiv:0803.2430v1. We illustrate each technique with applications.

math.QA↗