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arXiv · 1407.4060

Homology of depth-graded motivic Lie algebras and koszulity

Benjamin Enriquez·Pierre Lochak
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Abstract

The Broadhurst-Kreimer (BK) conjecture describes the Hilbert series of a bigraded Lie algebra A related to the multizeta values. Brown proposed a conjectural description of the homology of this Lie algebra (homological conjecture (HC)), and showed it implies the BK conjecture. We show that a part of HC is equivalent to a presentation of A, and that the remaining part of HC is equivalent to a weaker statement. Finally, we prove that granted the first part of HC, the remaining part of HC is equivalent to either of the following equivalent statements: (a) the vanishing of the third homology group of a Lie algebra with quadratic presentation, constructed out of the period polynomials of modular forms; (b) the koszulity of the enveloping algebra of this Lie algebra.

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BibTeXRIS

Benjamin Enriquez, Pierre Lochak. 2014-07-15. Homology of depth-graded motivic Lie algebras and koszulity. https://arxiv.org/abs/1407.4060

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