200 citations · 1.6k across the 65 of their papers we have counts for
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Langlands Duality and Poisson-Lie Duality via Cluster Theory and Tropicalization
Anton Alekseev, Arkady Berenstein, Benjamin Hoffman +1
Let be a connected semisimple Lie group. There are two natural duality constructions that assign to it the Langlands dual group and the Poisson-Lie dual group . T…
Poisson Structures and Potentials
Anton Alekseev, Arkady Berenstein, Benjamin Hoffman +1
We introduce a notion of weakly log-canonical Poisson structures on positive varieties with potentials. Such a Poisson structure is log-canonical up to terms dominated by the poten…
On the Kostant conjecture for Clifford algebra
Anton Alekseev, Anne Moreau
Let g be a complex simple Lie algebra, and h be a Cartan subalgebra. In the end of 1990s, B. Kostant defined two filtrations on h, one using the Clifford algebras and the odd analo…
Lie theory and the Chern-Weil homomorphism
A. Alekseev, E. Meinrenken
We introduce a canonical Chern-Weil map for possibly non-commutative g-differential algebras with connection. Our main observation is that the generalized Chern-Weil map is an alge…
Clifford algebras and the classical dynamical Yang-Baxter equation
A. Alekseev, E. Meinrenken
We describe a relationship of the classical dynamical Yang-Baxter equation with the following elementary problem for Clifford algebras: Given a vector space with quadratic form…