We give the classification of (co-)path Hopf algebras and semi-path Hopf algebras with pointed module structures. This leads to the classification of multiple crown algebras and multiple Taft algebras as well as kG-Yetter-Drinfeld modules and Nichols algebras with pointed module structures. Moreover, we characterize quantum enveloping algebras in terms of semi-path Hopf algebras. 2000 Mathemati...

We give the classification of (co-)path Hopf algebras and semi-path Hopf algebras with pointed module structures. This leads to the classification of multiple crown algebras and multiple Taft algebras as well as pointed Yetter-Drinfeld kG-modules and the corresponding Nichols algebras. Moreover, we characterize quantum enveloping algebras in terms of semi-path Hopf algebras.

OBJECTIVE The surgical Maze III procedure remains the gold standard in treating atrial fibrillation (AF); however due to clinical difficulties and higher risks, less invasive ablation alternatives are clinically investigated. The present study aims to define more efficient ablation patterns of the modified maze procedure using a biophysical model of human atria with chronic AF. METHODS A thre...

Let p be a prime number. It is known that any non-semisimple Hopf algebra of dimension p over an algebraically closed field of characteristic 0 is isomorphic to a Taft algebra. In this exposition, we will give a more direct alternative proof to this result.

(1) Acromegaly (Benoit, Theil, and Watten, 1963). (2) Paget's disease of bone (Benoit and others, 1963). (3) Hyperthyroidism (Sjoerdsma, Udenfriend, Keiser, and LeRoy, 1965). (4) Marfan's syndrome (Sjoerdsma, Davidson, Udenfriend, and Mitoma, 1958). (5) Hyperparathyroidism (Benoit and others, 1963; Laitinen, Nikkikii, and Kivirikko, 1966). (6) Primary and metastatic bone tumours (Hosley, Taft, ...