Loday's conjecture on Leibniz homology of the linear group

Let RR be a unital associative ring and let GL(R)\mathrm{GL}(R) denote its infinite linear group. Write HL(GL(R),k)\mathrm{HL}_{\bullet}(\mathrm{GL}(R),\Bbbk) for the Leibniz homology of this group. Loday's conjecture. The Leibniz homology of the linear group GL(R)\mathrm{GL}(R) is provided with a connected coZinbiel-associative bialgebra structure. This is the group-level counterpart of the coZinbiel-associative bialgebra structure appearing for Leibniz homology of matrix Lie algebras; the supplied text gives no evidence that the conjecture has been resolved.

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Primary source

Simon Covez, “Rack homology and conjectural Leibniz homology”, arXiv:1402.1625 (2014).

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