4 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…