Related papers: Infinity Algebras, Massey Products, and Deformatio…

We consider deformations of finite or infinite dimensional Lie algebras over a field of characteristic 0. There is substantial confusion in the literature if one tries to describe all the non-equivalent deformations of a given Lie algebra.…

Jae-Suk Park and the second-named author introduce the deformation problem of coisotropic submanifolds of a symplectic manifold as the study of Mauer-Cartan moduli problem of an $L_\infty$ algebra attached to the foliation de-Rham complex…

We use deformations of Lie algebra homomorphisms to construct deformations of dispersionless integrable systems arising as symmetry reductions of anti--self--dual Yang--Mills equations with a gauge group Diff$(S^1)$.

We consider degenerations of all simple Lie algebras of exceptional type obtained by embedding into affine Lie algebras. We give a filtration to consider this as an abelianisation of the original Lie algebra. We then show that the…

We give a geometric proof of inverse Hamiltonian reduction for all finite W-algebras in type $A$, a certain embedding of the finite W-algebra corresponding to an arbitrary nilpotent in $\mathfrak{gl}_N$ into that corresponding to a larger…

We show that the class of twisted fractionally Calabi-Yau algebras of finite global dimension coincides with the stable endomorphism algebras of $d$-cluster tilting modules over $d$-representation-finite algebras. This is an application of…

In this expository paper, we first review the classification of the restricted simple Lie algebras in characteristic different from 2 and 3 and then we describe their infinitesimal deformations. We conclude by indicating some possible…

Let $f:S\to B$ be a fibration of curves and let $f_\ast\omega_{S/B}=\cU\oplus \cA$ be the second Fujita decomposition of $f.$ In this paper we study a kind of Massey products, which are defined as infinitesimal invariants by the cohomology…

We propose a definition of deformed symmetrizable generalized Cartan matrices with several deformation parameters, which admit a categorical interpretation by graded modules over the generalized preprojective algebras in the sense of…

In this article, we discuss the relation between Kac-Moody algebras, the monstrous moonshine, Jacobi forms and infinite products. We also review Borcherds' solution of the Moonshine Conjecture and his work of constructing automorphic forms…

Let $\frak g$ be the finite dimensional simple Lie algebra associated to an indecomposable and symmetrizable generalized Cartan matrix $C=(a_{ij})_{n\times n}$ of finite type and let $\frak d$ be a finite dimensional Lie algebra related to…

Let $\L_m$ be the scheme of the laws defined by the Jacobi's identities on $\K^m$ with $\K$ a field. A deformation of $\g\in\L_m$, parametrized by a local $\K$-algebra $\A$, is a local $\K$-algebra morphism from the local ring of $\L_m$ at…

We study algebraic isomonodromic deformations of flat logarithmic connections on the Riemann sphere with $n\geq 4$ poles, for arbitrary rank. We introduce a natural property of algebraizability for the germ of universal deformation of such…

We consider classical and quantum one and two-dimensional systems with ladder operators that satisfy generalized Heisenberg algebras. In the classical case, this construction is related to the existence of closed trajectories. In…

We fix a prime p and construct new cases of pro-p extensions of number fields with restricted ramification and splitting, whose Galois groups decompose as coproducts of pro-p absolute Galois groups of local fields. As a consequence, these…

In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras.…

We study the category of finite--dimensional bi--graded representations of toroidal current algebras associated to finite--dimensional complex simple Lie algebras. Using the theory of graded representations for current algebras, we…

This paper studies the infinitesimal variation of the Lefschetz decomposition associated with a compatible sl_2-representation on a graded algebra. This allows to prove that the Jordan-Lefschetz property holds infinitesimally for the…

We give an interpretation of the $(q,t)$-deformed Cartan matrices of finite type and their inverses in terms of bigraded modules over the generalized preprojective algebras of Langlands dual type in the sense of Gei\ss-Leclerc-Schr\"{o}er…

We study certain Z_2-graded, finite-dimensional polynomial algebras of degree 2 which are a special class of deformations of Lie superalgebras, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the…