1,721,001 research outputs found
Small values and forbidden values for the Fourier antidiagonal constant of a finite group
Get PDFFor a finite group , let denote the Fourier norm of the
antidiagonal in . It was shown recently by the author (IMRN, 2023)
that coincides with the amenability constant of the Fourier
algebra of , and is equal to the normalized sum of the cubes of character
degrees of . Motivated by a gap result for amenability constants due to
Johnson (JLMS, 1994), we determine exactly which numbers in the interval
arise as values of .
As a by-product, we show that the set of values of does not
contain all its limit points. Some other calculations or bounds for are given for familiar classes of finite groups. We also indicate a
connection between and the commuting probability of , and use
this to show that every finite group satisfying must be solvable; here the value is best
possible.Comment: v3: AMS-LaTeX, 10pt mathpazo fonts; 18 pages. Corrections of some
mathematical typos, other minor improvements to phrasing. Submitted for
publicatio
Small values and forbidden values for the Fourier anti-diagonal constant of a finite group
No full textFor a finite group G, let AD(G) denote the Fourier norm of the antidiagonal in G × G. The author showed recently that AD(G) coincides with the amenability constant of the Fourier algebra of G and is equal to the normalized sum of the cubes of the character degrees of G. Motivated by a gap result for amenability constants by B. E. Johnson, we determine exactly which numbers in the interval [1,2] arise as values of AD(G). As a by-product, we show that the set of values of AD(G) does not contain all its limit points. Some other calculations or bounds for AD(G) are given for familiar classes of finite groups. We also indicate a connection between AD(G) and the commuting probability of G, and use this to show that every finite group G satisfying AD(G) < 61/15 must be solvable; here, the value 61/15 is the best possible
Splitting maps and norm bounds for the cyclic cohomology of biflat Banach algebras
Get PDFWe revisit the old result that biflat Banach algebras have the same cyclic cohomology as C, and obtain a quantitative variant (which is needed in forthcoming joint work of the author). Our approach does not rely on the Connes-Tsygan exact sequence, but is motivated strongly by its construction as found in [Connes,1985] and [Helemskii,1992]
Simplicial homology of strong semilattices of Banach algebras
No full textCertain semigroups are known to admit a 'strong semilattice decomposition' into simpler pieces. We introduce a class of Banach algebras that generalise the l1-convolution algebras of such semigroups, and obtain a disintegration theorem for their simplicial homology. Using this we show that for any Clifford semigroup S of amenable groups, l1(S) is simplicially trivial: this generalises previous results of the author (Glasgow Math. Journal, 2006). Some other applications are presented
On amenability constants of Fourier algebras : new bounds and new examples
No full textLet be a locally compact group. If is finite then the amenability constant of its Fourier algebra, denoted by , admits an explicit formula [Johnson, JLMS 1994]; if is infinite then no such formula for is known, although lower and upper bounds were established by Runde [PAMS 2006]. Using non-abelian Fourier analysis, we obtain a sharper upper bound for when is discrete. Combining this with previous work of the first author [Choi, IMRN 2023], we exhibit new examples of discrete groups and compact groups where can be calculated explicitly; previously this was only known for groups that are products of finite groups with "degenerate"' cases. Our new examples also provide additional evidence to support the conjecture that Runde's lower bound for the amenability constant is in fact an equality
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
Simplicial cohomology of augmentation ideals in
Get PDFLet G be a discrete group. We give a decomposition theorem for the Hochschild cohomology of l1(G) with coefficients in certain G-modules. Using this we show that if G is commutative-transitive, the canonical inclusion of bounded cohomology of G into simplicial cohomology of l1(G) is an isomorphism
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
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