9 problems

In 1977, Kac classified the finite-dimensional Lie superalgebras, while Cartan's list of infinite-dimensional Lie algebras is $(W_n,S_n,H_n,K_n)$. Kac's conjecture. The infinite-di…

The classical Grassmannian carries an action of the Virasoro algebra, and the moduli space of curves is considered with respect to this action. In the super setting, one analogousl…

Let $\widehat{\mathfrak{b}}$ be the algebra whose modules are under consideration, and let $\widehat{V}$ and $\widehat{W}$ be the $\widehat{\mathfrak{b}}$-submodules appearing in t…

Let $R$ be a Lie conformal algebra, and let $\mathcal{R}$ be a vertex manifold. Write $\operatorname{Conf}(\mathcal{R})$ for the Lie conformal algebra associated with $\mathcal{R}$…

The three-dimensional Maxwell and AdS-Lorentz supergravity theories presented in the cited works admit new infinite-dimensional structures obtained through the corresponding…

The $\mathcal{N}$-extended Maxwell superalgebra is the finite-dimensional symmetry algebra underlying the three-dimensional Chern–Simons supergravity theories considered here. The…

Isomorphism conjecture. The algebra ${\mathcal A}_q$ is conjectured to be isomorphic to the q-Onsager algebra.

Let $\mathbf Q$ be the 3-generated Lie superalgebra introduced in Pe16. A Lie superalgebra is just infinite if it is infinite-dimensional and every nonzero ideal has finite codimen…

Let $\mathcal E^+$ be the subalgebra of the quantum continuous $\mathfrak{gl}_\infty$ algebra $\mathcal E$ generated by the elements $e_i$, $i\in\mathbb Z$, and let ${\bf S}$ be th…