Glider Representations

Glider Representations offer several applications across different fields within Mathematics, thereby motivating the introduction of this new glider theory and opening numerous doors for future research, particularly with respect to more complex filtration chains. Features • Introduces new concepts in the Theory of Rings and Modules • Suitable for researchers and graduate students working in this area, and as supplementary reading for courses in Group Theory, Ring Theory, Lie Algebras and Sheaf Theory • The first book to explicitly outline this new approach to gliders and fragments and associated concepts I General fragment and glider theory Chapter 1: Basic de nitions and generalities. Chapter 2: Basic properties. Chapter 3: Irreducible fragments and gliders. II Right bounded algebra ltrations. Chapter 4: Glider representation theory of a chain of nite groups. Chapter 5: Glider representation rings of nite groups and glider character theory. Chapter 6: Chains of semisimple Lie algebras. III Unbounded and standard ltrations. Chapter 7: Sheaves of glider representations. Chapter 8: Glider Brauer-Severi varieties. Chapter 9: Odds and ends. Frederik Caenepeel is a postdoctoral researcher at the Shanghai Center for Mathematical Sciences associated to Fudan University, Shanghai, China. He received his PhD degree from the University of Antwerp, Belgium under the supervision of Professor, Doctor Wendy Lowen and Emeritus Professor, Doctor Fred Van Oystaeyen. In his free time, Frederik enjoys doing outdoor sports activities, discovering the world and catching up with friends. Fred Van Oystaeyen is an emeritus Professor at the University of Antwerp. His research interests include Non-commutative Algebra and Geometry, Hopf Algebras, graded rings, the Brauer group and representation theory. He has authored or co-authored over 300 scientific paper, about 25 research books and edited several proceedings of the more than 60 international congresses. He did his research evaluation in several countries, was president of the Belgian Science Foundation's math committee and served 5 years on the Academic Advisory Committee for the ERASMUS program. He was also a visiting scholar at the University of Cambridge (UK) and honorary professor at the Beijing Normal University. In his free time, he enjoys Blues music and caudiciform plants, cacti and bonsai trees.