1,722,041 research outputs found
The Interplay of R-matrices and Quantum Groups
No full textThese are the expanded lecture notes of a mini-course given by the author in Milan in June 2024, during the conference GABY: Groups and Algebras in Bicocca for Young algebraists. We present a concise introduction to the theory of quantum groups, focusing on their ability to produce solutions of the quantum Yang-Baxter equation
Coxeter categories and quantum groups
Full text linkWe define the notion of braided Coxeter category, which is informally a monoidal category carrying compatible, commuting actions of a generalised braid group B_W and Artin’s braid groups B_n on the tensor powers of its objects. The data which defines the action of B_W bears a formal similarity to the associativity constraints in a monoidal category, but is related to the coherence of a family of fiber functors. We show that the quantum Weyl group operators of a quantised Kac–Moody algebra U_{\hbar }{{\mathfrak {g}}}, together with the universal R-matrices of its Levi subalgebras, give rise to a braided Coxeter category structure on integrable, category {\mathcal {O}}-modules for U_{\hbar }{{\mathfrak {g}}}. By relying on the 2-categorical extension of Etingof–Kazhdan quantisation obtained in Appel and Toledano Laredo (Selecta Math NS 24:3529–3617, 2018), we then prove that this structure can be transferred to integrable, category {\mathcal {O}}-representations of {\mathfrak {g}}. These results are used in Appel and Toledano Laredo (arXiv:1512.03041, p 48, 2015) to give a monodromic description of the quantum Weyl group operators of U_{\hbar }{{\mathfrak {g}}}, which extends the one obtained by the second author for a semisimple Lie algebra
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Full text link“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
Full text linkWe 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
Uniqueness of Coxeter structures on Kac–Moody algebras
Full text linkAbstract. Let g be a symmetrisable Kac–Moody algebra, and Ung the corresponding quantum group. We showed in [1, 2] that the braided Coxeter structure on integrable, category O representations of Ung which underlies the R–matrix actions arising from the Levi subalgebras of Ung and the quantum Weyl group action of the generalised braid group Bg can be transferred to integrable, category O representations of g. We prove in this paper that, up to unique equivalence, there is a unique such structure on the latter category with prescribed restriction functors, R–matrices, and local monodromies. This extends, simplifies and strengthens a similar result of the second author valid when g is semisimple, and is used in [3] to describe the monodromy of the rational Casimir connection of g in terms of the quantum Weyl group operators of Ung. Our main tool is a refinement of Enriquez’s universal algebras, which is adapted to the PROP describing a Lie bialgebra graded by the non–negative roots of g.<br/
Reinhold Niebuhr, Faith and History. New-York, Charles Scribner’s Sons, 1949
No full textAppel A. Reinhold Niebuhr, Faith and History. New-York, Charles Scribner’s Sons, 1949. In: Revue d'histoire et de philosophie religieuses, 32e année n°2,1952. pp. 150-152
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