Report Title：An introduction to the theory of coalgebras
Reporter：Maxim Goncharov
Affiliation: Sobolev Institute of Mathematics
Report Time: 15:30-16:30 July 15-18, 20-23, 2026
Report Location: Zoom Id: 904 645 6677，Password: 2026
Abstract:
Main purposes of the course are to introduce the foundations of the theory of coalgebras (that is considered as a part of the theory of Hopf algebras), as well as to acquire an experience in working with coalgebras that will simplify the future deeper study in this area. Namely, we will discuss basic concepts and main examples of coalgebras, comodules, the dual coalgebra and the final dual coalgebra of an algebra.
Indicative course program:
1. Tensor product of vector spaces.
2. Definition of coalgebras. Basic examples.
3. Subcoalgebras and coideals. The Fundamental Theorem of Coalgebras.
4. The factor coalgebra. Group-like elements.
5. The dual (co)algebra.
6. The finite dual of an algebra.
7. Comodules. The fundamental Theorem of Comodules.
8. Rational modules
Bio:
Maxim Goncharov: PhD, a senior research fellow of the Sobolev Institute of Mathematics and an associate professor of Novosibirsk State University. Maxim Goncharov specializes in the study of nonassociative rings and algebras, nonassociative bialgebras, Lie bialgebras, Malcev bialgebras, classical Yang-Baxter equations, Rota-Baxter operators, Hopf algebras and quantum groups.
