相关论文: Dg Loday-Pirashvili modules over Lie algebras

We extend the techniques in arXiv:2209.08865(1) to the non-simply-laced situation, and calculate explicit special values of parabolic affine inverse Kazhdan-Lusztig polynomials for subregular nilpotent orbits. We thus obtain explicit…

In this paper, we present a canonical quantization of Lie bialgebra structures on the formal power series $\mathfrak{d}[\![t]\!]$ with coefficients in the cotangent Lie algebra $\mathfrak{d} = T^*\mathfrak{g} = \mathfrak{g} \ltimes…

In this paper we construct a large class of modules for toroidal Lie superalgebras. Toroidal Lie superalgebras are universal central extension of G tensor A where G is a basic classical Lie superalgebra and A is a Laurent polynomial ring in…

By direct calculations of matrix form of super Jacobi and mixed super Jacobi identities which are obtained from adjoint representation, and using the automorphism supergroup of the gl(1|1) Lie superalgebra, we determine and classify all…

We show that the definition of unrolled Hopf algebras can be naturally extended to the Nichols algebra $\mathcal{B}$ of a Yetter-Drinfeld module $V$ on which a Lie algebra $\mathfrak g$ acts by biderivations. Specializing to Nichols…

The notion of Lie algebroids over a topological ringed space provides a unified framework to study various geometric structures. This geometric concept is intimately connected with well-known algebraic structures, including Gerstenhaber…

A discrete group which admits a faithful, finite dimensional, linear representation over a field $\mathbb F$ of characteristic zero is called linear. This note combines the natural structure of semi-direct products with work of A. Lubotzky…

We investigate the existence of left-invariant closed G$_2$-structures on seven-dimensional non-solvable Lie groups, providing the first examples of this type. When the Lie algebra has trivial Levi decomposition, we show that such a…

The simple 7-dimensional Malcev algebra $M$ is isomorphic to the irreducible $\mathfrak{sl}(2,\mathbb{C})$-module V(6) with binary product $[x,y] = \alpha(x \wedge y)$ defined by the $\mathfrak{sl}(2,\mathbb{C})$-module morphism…

The so called theory of derived D-modules is an extension of classical D-modules to derived algebraic geometry, which uses the derived information of the base scheme. We prove that the three different definitions of derived D-modules, given…

Given a Lie algebra $\mathfrak g$ and a $\mathfrak{g}$-module $V$, it is due to Gerstenhaber that there is an isomorphism between $H^3(\mathfrak{g}, V )$ and the group of equivalence classes of crossed modules with kernel $V$ and cokernel…

In this paper, we introduce the notion of completely non-trivial module of a Lie conformal algebra. By this notion, we classify all finite irreducible modules of a class of $\mathbb{Z}^+$-graded Lie conformal algebras…

A two-dimensional chiral conformal field theory can be viewed mathematically as the representation theory of its chiral algebra, a vertex operator algebra. Vertex operator algebras are especially well suited for studying logarithmic…

A study is made of left-invariant $\mathrm{G}_2$-structures with an exact 3-form on a Lie group $G$ whose Lie algebra $\mathfrak{g}$ admits a codimension-one nilpotent ideal $\mathfrak{h}$. It is shown that such a Lie group $G$ cannot admit…

In this paper, we classify all simple Harish-Chandra modules over the super affine-Virasoro algebra $\widehat{\mathcal{L}}=\mathcal{W}\ltimes(\mathfrak{g}\otimes \mathcal{A})\oplus \mathbb{C}C$, where $\mathcal{A}=\mathbb{C}[t^{\pm…

Let g=g_{0} \oplus g_{1} be a classical Lie superalgebra and F be the category of finite dimensional g-supermodules which are semisimple over g_{0}. In this paper we investigate the homological properties of the category F. In particular we…

A Lie algebroid on a variety X/k is an extension \alpha: g_X \to T_X of the tangent sheaf both as O_X-module and Lie algebra over the base field, with the obvious compatibilities; and given a Lie algebroid one has its associated ring of…

For an associative algebra $A$, the famous theorem of Loday, Quillen and Tsygan says that there is an isomorphism between the graded symmetric product of the cyclic homology of $A$ and the Lie algebra homology of the infinite matrices…

Let G be a reductive group over an algebraically closed field k of very good characteristic. The Lusztig-Vogan bijection is a bijection between the set of dominant weights for G and the set of irreducible G-equivariant vector bundles on…

We study {\em disemisimple} Lie algebras, i.e., Lie algebras which can be written as a vector space sum of two semisimple subalgebras. We show that a Lie algebra $\mathfrak{g}$ is disemisimple if and only if its solvable radical coincides…