V. Dotsenko

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math.RA2025

Algebraic versions of $T^{2}$ and of $P^{1} \times P^{1}$ 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…

math.RA2025

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 $G L_{d}$ -module structure of the free $d$ -generated Jordan algebra. Thei…

math.RA2025

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 $G L_{d}$ -module structure of the free…

Algebraic versions of T2 and of P1×P1 and Hochschild cohomology

On the conjecture of Kashuba and Mathieu about free Jordan algebras

On the conjecture of Shang about free alternative algebras

Algebraic versions of $T^{2}$ and of $P^{1} \times P^{1}$ and Hochschild cohomology