Hopf algebra

The above observations encourage us to summarize fundamental physics, where applied the normed division algebra and its cousins (Hopf maps and Hurwitz transformations) as the basic mathematical language.

23p vispiderman 15-06-2023 4 2   Download

In this paper, we intend to study idempotents of the Green algebra (complexified Green ring) of any finite dimensional pointed rank one Hopf algebra of nilpotent type over the complex number field. We first determine all one dimensional representations of the quotient algebra of the Green algebra modulo its Jacobson radical.

17p danhdanh27 07-01-2019 15 2   Download

In this work, we give a characterization of free crossed modules and also get a relation between projective crossed modules and the cyclic homology of associative algebras by using Hopf-type formulas.

9p danhdanh27 07-01-2019 28 2   Download

Codes over the finite sub-Hopf algebras A(n) of the (mod 2) Steenrod algebra A were studied by Dougherty and Vergili. In this paper we study some Euclidean and Hermitian self-dual codes over A(n) by considering Milnor basis elements.

10p danhdanh27 07-01-2019 13 1   Download

Using a variety of methods developed in the literature (in particular, the theory of weak Hopf algebras), we prove a number of general results about fusion categories in characteristic zero. We show that the global dimension of a fusion category is always positive, and that the S-matrix of any (not necessarily hermitian) modular category is unitary. We also show that the category of module functors between two module categories over a fusion category is semisimple, and that fusion categories and tensor functors between them are undeformable (generalized Ocneanu rigidity).

63p noel_noel 17-01-2013 46 5   Download

The present book collects most of the courses and seminars delivered at the meeting entitled “ Frontiers in Number Theory, Physics and Geometry”, which took place at the Centre de Physique des Houches in the French Alps, March 9- 21, 2003. It is divided into two volumes. Volume I contains the contributions on three broad topics: Random matrices, Zeta functions and Dynamical systems. The present volume contains sixteen contributions on three themes: Conformal field theories for strings and branes, Discrete groups and automorphic forms and finally, Hopf algebras and renormalization....

0p camnhung_1 13-12-2012 77 5   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Superization and (q, t)-specialization in combinatorial Hopf algebras...

46p thulanh8 19-09-2011 55 2   Download