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Bilinear Forms on the Green Rings of Finite Dimensional Hopf Algebras
No full textIn this paper, we study the Green ring and the stable Green ring of a finite dimensional Hopf algebra by means of bilinear forms. We show that the Green ring of a Hopf algebra of finite representation type is a Frobenius algebra over Z with a dual basis associated to almost split sequences. On the stable Green ring we define a new bilinear form which is more accurate to determine the bi-Frobenius algebra structure on the stable Green ring. We show that the complexified stable Green algebra is a group-like algebra, and hence a bi-Frobenius algebra, if the bilinear form on the stable Green ring is non-degenerate.The authors would like to thank the referees for their careful reading of this article and for valuable comments. The first author was funded by Postdoctoral Science Foundation of China (Grant No. 2017M610316), the second author was funded by the NSF of China (Grant No. 11871063).Wang, ZH (reprint author), Taizhou Univ, Dept Math, Taizhou 225300, Peoples R China.
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Construct bi-frobenius algebras via the Benson-Carlson quotient rings
No full textLet H be a finite dimensional spherical Hopf algebra, r(H) the Green ring of H and P the ideal of r(H) generated by all H-modules of quantum dimension zero. Using dimensions of negligible morphism spaces, we define a bilinear form on the Green ring r(H). This form is associative, symmetric and its radical is annihilator of a certain central element of r(H). After that we consider the Benson-Carlson quotient ring r(H)/P of r(H). This quotient ring can be thought of as the Green ring of a factor category of H-module category. Moreover, if H is of finite representation type, the Benson-Carlson quotient ring admits group-like algebra as well as bi-Frobenius algebra structure
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
Green rings of finite dimensional pointed Hopf algebras of rank one
No full textIn deze thesis bestuderen we Green ringen van eindig dimensionale pointed Hopf algebras van rang één over een algebraïsch gesloten veld k met karakteristiek 0. Verder proberen we de verworven eigenschappen van Green ringen van pointed Hopf algebras van rang één te veralgemenen voor eindig dimensionale Hopf algebras. In Hoofdstuk 2 en Hoofdstuk 3 werken we met eindig dimensionale pointed Hopf algebras van rang één (van het nilpotente type en het niet-nilpotente type, respectievelijk). We vertonen de Green ring van een dergelijke Hopf algebra in termen van voortbrengers en relaties, waaruit we kunnen besluiten dat de Green ring commutatief en symmetrisch is met een duale basis geassocieerd aan bepaalde bijna split rijen. Het blijkt dat het Jacobson radicaal van de Green ring een hoofd-ideaal is, voortgebracht door een speciaal element voorgesteld door een lineaire combinatie van projectieve modulen, en dat de idempotenten van de Green ring triviaal zijn. Bovendien zijn de niet-triviale idempotenten van de gecomplexifieerde Green ring van een pointed Hopf algebra van rang één van het nilpotente type volledig bepaald. In Hoofdstuk 4 bestuderen we de stabiele Green ring (i.e., de Green ring van de stabiele categorie) van een eindig dimensionale pointed Hopf algebra van rang één. We tonen aan dat de stabiele Green ring overeenkomt met het quotient van de Green ring van H modulo het ideaal voortgebracht door alle projectieve modulen. Daarenboven, de gecomplexifieerd stabiele Green ring is een groepachtige algebra, en bijgevolg een bi-Frobenius algebra. In Hoofdstuk 5 bestuderen we de Green ring van een willekeurige eindig dimensionale Hopf algebra H. Ten eerste onderzoeken we kwantum dimensies van indecomposabele H-modulen. Hierdoor kunnen we een antwoord geven op de vraag van Cibils. Vervolgens bestuderen we enkele ringtheoretische eigenschappen van de Green ring r(H) van H, waaronder de beschrijvingen van zekere belangrijke eenzijdige idealen, de nilpotente idealen en de centrale primitieve idempotenten van r(H). Bovendien bewijzen we dat de stabiele Green ring van H een associatieve non-degenerate bi-lineaire vorm bezit die geïnduceerd wordt door de bi-lineaire vorm op r(H). Ten slotte, indien H een sferische Hopf algebra is, vormt de quotiënt categorie van H-modulen modulo alle verwaarloosbare morfismen een addititieve semisimpele sferische monoïdale categorie. We tonen aan dat de Green ring van de quotiënt categorie isomorf is met de quotiënt ring van r(H) modulo alle indecomposabele modulen met kwamtum dimensie nul. In het bijzonder, indien H van het eindige representatie type is, dan is de gecomplexifieerd quotiënt ring een groepachtige algebra, en bijgevolg een bi-Frobenius algebra.Let H-mod be the category of finite dimensional representations of a Hopf algebra H over a field k. In the study of the monoidal structure of H-mod one has to consider the decompositions of the tensor product of representations in H-mod. In particular, the decomposition of the tensor product of any two indecomposable representations in H-mod. However, in general, very little is known about how a tensor product of two indecomposable representations decomposes into a direct sum of indecomposable representations. One method of addressing this problem is to consider the tensor product as the multiplication of the Green ring (or the representation ring) r(H) of H, and to study the ring-theoretical properties of the Green ring
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