Titlebook: Classical Hopf Algebras and Their Applications; Pierre Cartier,Frédéric Patras Book 2021 Springer Nature Switzerland AG 2021 Hopf algebras

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Kelly Digby Peebles,Gabriella ScarlattaThis chapter is dedicated to the structure of graded connected commutative or cocommutative Hopf algebras. Our approach is based on the properties of their descent gebras, from which many results pertaining to the classical theory of free Lie algebras can be recovered and extended to statements on the structure of graded Hopf algebras.

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Representing the Modern Animal in CultureHopf algebras were first introduced in relation to the homology of groups and more generally of topological spaces equipped with a product. This chapter surveys some of the main applications of Hopf algebras in the field. Contrary to the rest of the volume, various results are considered over a field of finite characteristic.

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Coalgebras, DualityThe Chapter deals with coalgebras, comodules, duality, representative functions, and structural properties of endomorphisms (notions of pseudo- and quasi-coproducts).

精密

Hopf Algebras and GroupsIn this chapter, we introduce bialgebras and Hopf algebras, as well as various fundamental related notions and constructions. We discuss briefly their relations to algebraic groups and enveloping algebras that will be detailed later in this book.

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