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Asymptotics for Capelli polynomials with involution
Get PDFLet F be the free associative algebra with involution ∗ over a field F of characteristic zero. We study the asymptotic behavior of the sequence of ∗- codimensions of the T-∗-ideal Γ∗ M+1,L+1 of F generated by the ∗-Capelli polynomials Cap∗ M+1[Y, X] and Cap∗ L+1[Z, X] alternanting on M + 1 symmetric variables and L + 1 skew variables, respectively. It is well known that, if F is an algebraic closed field of characteristic zero, every finite dimensional ∗-simple algebra is isomorphic to one of the following algebras: · (Mk(F ), t) the algebra of k × k matrices with the transpose involution; · (M2m(F ), s) the algebra of 2m × 2m matrices with the symplectic involution; · (Mh(F ) ⊕ Mh(F )op, exc) the direct sum of the algebra of h × h matrices and the opposite algebra with the exchange involution. We prove that the ∗-codimensions of a finite dimensional ∗-simple algebra are asymptotically equal to the ∗-codimensions of Γ∗ M+1,L+1, for some fixed natural numbers M and L. In particular: c∗n(Γ∗k(k+1)2 +1, k(k2−1) +1) ≃ c∗ n((Mk(F ), t)); c∗n(Γ∗ m(2m−1)+1,m(2m+1)+1) ≃ c∗ n((M2m(F ), s)); and c∗n(Γ∗ h2+1,h2+1) ≃ c∗ n((Mh(F ) ⊕ Mh(F )op, exc)) Moreover the exact asymptotics of c∗n((Mk(F),t)) and c∗n((M2m(F),s)) are known and those of (Mh(F)⊕Mh(F)op,exc) can be easily deduced
Capelli identities on algebras with involution or graded involution
Get PDFWe present recent results about Capelli polynomials with involution or graded involution and their asymptotics. In the associative case, the asymptotic equality between the codimensions of the T -ideal generated by the Capelli
polynomial of rank k2 + 1 and the codimensions of the matrix algebra Mk(F) was proved. This result was extended to
superalgebras. Recently, similar results have been determined by the authors in the case of algebras with involution and
superalgebras with graded involution
ON THE ASYMPTOTICS OF CAPELLI POLYNOMIALS
No full textAbstract. We present old and new results about Capelli polynomials, Z2-graded Capelli
polynomials and Capelli polynomials with involution and their asymptotics.
Let Capm = Pσ2Sm (sgnσ)tσ(1)x1tσ(2) · · · tσ(m−1)xm−1tσ(m) be the m-th Capelli
polynomial of rank m. In the ordinary case (see [33]) it was proved the asymptotic
equality between the codimensions of the T -ideal generated by the Capelli polynomial
Capk2+1 and the codimensions of the matrix algebra Mk(F ). In [9] this result was
extended to superalgebras proving that the Z2-graded codimensions of the T2-ideal generated by the Z2-graded Capelli polynomials Cap0 M+1 and Cap1 L+1 for some fixed M,
L, are asymptotically equal to the Z2-graded codimensions of a simple finite dimensional
superalgebra. Recently, the authors proved that the ∗-codimensions of a ∗-simple finite dimensional algebra are asymptotically equal to the ∗-codimensions of the T-∗-ideal
generated by the ∗-Capelli polynomials Cap+ M+1 and Cap− L+1, for some fixed natural
numbers M and L
Valenti, Angela
No full textCentro Asturiano membership record of Angela Valenti; Socio Number: 1387.https://digitalcommons.usf.edu/asturiano_membership/5977/thumbnail.jp
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
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