Relations between elliptic multiple zeta values and a special derivation algebra

Journal article

We investigate relations between elliptic multiple zeta values (eMZVs) and describe a method to derive the number of indecomposable elements of given weight and length. Our method is based on representing eMZVs as iterated integrals over Eisenstein series and exploiting the connection with a special derivation algebra. Its commutator relations give rise to constraints on the iterated integrals over Eisenstein series relevant for eMZVs and thereby allow to count the indecomposable representatives. Conversely, the above connection suggests apparently new relations in the derivation algebra. Under https://tools.aei.mpg.de/emzv we provide relations for eMZVs over a wide range of weights and lengths.

Authors: Broedel, J; Matthes, N; Schlotterer, O

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: Journal of Physics A: Mathematical and Theoretical
• Volume: 49
• Issue: 15
• Pages: ARTN 155203
• Publication date: 2016-03-02
• Acceptance date: 2016-01-04
• DOI: 10.1088/1751-8113/49/15/155203
• EISSN: 1751-8121
• ISSN: 1751-8113
• Keywords: elliptic multiple zeta value; iterated integrals; string-theory one-loop amplitude; derivation algebra; SBTMR