7 research outputs found
Quantum groups: from Kulish-Reshetikhin discovery to classification
The aim of this paper is to provide an overview of the results about
classification of quantum groups that were obtained in arXiv:1303.4046
[math.QA] and arXiv:1502.00403 [math.QA].Comment: 10 page
Classification of quantum groups and Belavin--Drinfeld cohomologies for orthogonal and symplectic Lie algebras
In this paper we continue to study Belavin-Drinfeld cohomology introduced in
arXiv:1303.4046 [math.QA] and related to the classification of quantum groups
whose quasi-classical limit is a given simple complex Lie algebra. Here we
compute Belavin-Drinfeld cohomology for all non-skewsymmetric -matrices from
the Belavin-Drinfeld list for simple Lie algebras of type , , and .Comment: 17 page
Fra\"iss\'e limits of C*-algebras
We realize the Jiang-Su algebra, all UHF algebras, and the hyperfinite
II factor as Fra\"iss\'e limits of suitable classes of structures.
Moreover by means of Fra\"iss\'e theory we provide new examples of AF algebras
with strong homogeneity properties. As a consequence of our analysis we deduce
Ramsey-theoretic results about the class of full-matrix algebras.Comment: 19 pages. Final submitted versio
Fraïssé limits of C*-algebras
We realize the Jiang-Su algebra, all UHF algebras, and the hyperfinite II_1 factor as Fraïssé limits of suitable classes of structures. Moreover by means of Fraïssé theory we provide new examples of AF algebras with strong homogeneity properties. As a consequence of our analysis we deduce Ramsey-theoretic results about the class of full-matrix algebras
Some remarks on vector-valued integration
The paper continues the study of the notion of Riemann–Lebesgue integral, which was introduced before by two of the authors. The result about the convexity of the limit set of integral sums is generalized to the case of weakly-compactly generated spaces. The notion of Riemann–Lebesgue integral is used to introduce new classes of Banach spaces. The properties of these new spaces are studied