Kontsevich and Takhtajan construction of star product on the Poisson Lie group GL(2)

TL;DR

This paper compares Takhtajan's star product on the Poisson-Lie group GL(2) with Kontsevich's graph-based star products and demonstrates they are not equivalent through direct computation.

Contribution

It provides a direct computational comparison showing Takhtajan's star product cannot be expressed as a Kontsevich graph-based star product on GL(2).

Findings

Takhtajan's star product on GL(2) is not a K-star product.

Direct computation confirms the non-equivalence.

Clarifies the relationship between different star product constructions.

Abstract

Comparing the star product defined by Takhtajan on the Poisson-Lie group GL(2) and any star product calculated from the Kontsevich's graphs (any ''K-star product'') on the same group, we show, by direct computation, that the Takhtajan star product on GL(2) can't be written as a K-star product.