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The Kashiwara-Vergne conjecture and Drinfeld's associators | Anton Alekseev
; Charles Torossian
; | Date: |
28 Feb 2008 | Abstract: | The Kashiwara-Vergne (KV) conjecture is a property of the Campbell-Hausdorff
series put forward in 1978. It has been settled in the positive by E.
Meinrenken and the first author in 2006. In this paper, we study the uniqueness
issue for the KV problem. To this end, we introduce a family of infinite
dimensional groups KV_n, and an extension hat{KV}_2 of the group KV_2. We show
that the group hat{KV}_2 contains the Grothendieck-Teichmueller group GRT as a
subgroup, and that it acts freely and transitively on the set of solutions of
the KV problem Sol(KV). Furthermore, we prove that Sol(KV) is isomorphic to a
direct product of a line k (k being a field of characteristic zero) and the
set of solutions of the pentagon equation with values in the group KV_3. The
latter contains the set of Drinfeld’s associators as a subset. As a by-product,
we obtain a new proof of the Kashiwara-Vergne conjecture based on the
Drinfeld’s theorem on existence of associators. | Source: | arXiv, 0802.4300 | Services: | Forum | Review | PDF | Favorites |
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