Coset decomposition for semisimple Hopf algebras
S. Burciu
TL;DR
This paper introduces a double coset concept for semisimple finite-dimensional Hopf algebras using an equivalence relation on irreducible characters, providing formulas for character restriction to normal subalgebras.
Contribution
It presents a novel double coset framework for semisimple Hopf algebras and derives new formulas for irreducible character restrictions.
Findings
Defined double coset equivalence relation on irreducible characters
Derived formulas for restricting irreducible characters to normal Hopf subalgebras
Extended classical coset concepts to the Hopf algebra setting
Abstract
The notion of double coset for semisimple finite dimensional Hopf algebras is introduced. This is done by considering an equivalence relation on the set of irreducible characters of the dual Hopf algebra. As an application formulae for the restriction of the irreducible characters to normal Hopf subalgebras are given.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Algebra and Logic · Algebraic structures and combinatorial models