Non-commutative generalized Dedekind symbols

TL;DR

This paper introduces generalized Dedekind symbols valued in non-commutative groups, extending previous work by incorporating iterated period integrals of modular forms, thereby broadening the algebraic framework of these symbols.

Contribution

It generalizes Dedekind symbols to non-commutative groups using iterated period integrals, expanding the algebraic and analytical scope of the theory.

Findings

Construction of non-commutative Dedekind symbols

Examples using iterated period integrals of modular forms

Extension of previous commutative frameworks

Abstract

We define and study generalized Dedekind symbols with values in non--necessarily commutative groups, generalizing constructions of Sh. Fukuhara in [Fu1], [Fu2]. Basic examples of such symbols are obtained by replacing period integrals of modular forms (cf. [Ma1], [Ma2], [Kn1], [Kn2], [ChZ]) by iterated period integrals introduced and studied in [Ma3], [Ma4].