On complements and the factorization problem for Hopf algebras
Sebastian Burciu
TL;DR
This paper introduces new results on complements in semisimple Hopf algebras, extending classical group theory results, and proves the uniqueness of certain decompositions for these algebras.
Contribution
It extends known group theory results to semisimple Hopf algebras and establishes the uniqueness of Krull-Schmidt type decompositions.
Findings
New results on complements in semisimple Hopf algebras
Extension of classical group theory results
Proof of uniqueness of Krull-Schmidt type decompositions
Abstract
Two new results concerning complements in a semisimple Hopf algebra are proved. They extend some well known results from group theory. The uniqueness of Krull Schmidt Remak type decomposition is proved for semisimple completely reducible Hopf algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons