18 citations · 18 across the 7 of their papers we have counts for
8 papers
Algebraic versions of and of and Hochschild cohomology
Vladimir Dotsenko, Andrea Solotar
We examine the Hochschild cohomology for triangular algebras that capture some aspects of geometry and topology of the torus and of the quadric surface, and for deformations of the…
On the conjecture of Kashuba and Mathieu about free Jordan algebras
Vladimir Dotsenko, Irvin Roy Hentzel
Kashuba and Mathieu proposed a conjecture on vanishing of Lie algebra homology, implying a description of the -module structure of the free -generated Jordan algebra. Thei…
On the conjecture of Shang about free alternative algebras
Vladimir Dotsenko
Kashuba and Mathieu proposed a conjecture on vanishing of some components of the homology of certain Lie algebras, implying a description of the -module structure of the free…
Global Weyl modules for thin Lie algebras are finite-dimensional
Vladimir Dotsenko, Sergey Mozgovoy
The notion of Weyl modules, both local and global, goes back to Chari and Pressley in the case of affine Lie algebras, and has been extensively studied for various Lie algebras gra…
Hidden structures behind ambient symmetries of the Maurer-Cartan equation
Vladimir Dotsenko, Sergey Shadrin
For every differential graded Lie algebra one can define two different group actions on the Maurer-Cartan elements: the ubiquitous gauge action and the action of $\m…
Stable homology of Lie algebras of derivations and homotopy invariants of wheeled operads
Vladimir Dotsenko
We prove a theorem that computes, for any augmented operad , the stable homology of the Lie algebra of derivations of the free algebra with twisted bi…
The three graces in the Tits--Kantor--Koecher category
Vladimir Dotsenko, Iryna Kashuba
A metaphor of Loday describes Lie, associative, and commutative associative algebras as ``the three graces'' of the operad theory. In this article, we study the three graces in the…
Compatible associative products and trees
Vladimir Dotsenko
We compute dimensions of graded components for free algebras with two compatible associative products, and give a combinatorial interpretation of these algebras in terms of planar…