Related papers: Stable flatness of nonarchimedean hyperenveloping …

This article describes an entirely algebraic construction for developing conformal geometries, which provide models for, among others, the Euclidean, spherical and hyperbolic geometries. On one hand, their relationship is usually shown…

Let $G$ be a split connected reductive group over the ring of integers of a finite unramified extension $K$ of $\mathbf{Q}_p$. Under a standard assumption on the Coxeter number of $G$, we compute the cohomology algebra of $G(\mathcal{O}_K)$…

Let $U$ be the enveloping algebra of a finite dimensional nonabelian Lie algebra $\mathfrak{g}$ over a field of characteristic zero. We show that there is an open nonempty open subset $X$ of $U_1 = \mathfrak{g}\oplus K$ such that $U/Ux$ is…

Let $(\mathcal{M}, Q)$ be a dg manifold. The space of vector fields with shifted degrees $(\mathcal{X}(\mathcal{M})[-1], L_Q)$ is a Lie algebra object in the homology category $\mathrm{H}((C^{\infty}_{\mathcal{M}},Q)\mathrm{-}\mathbf{mod})$…

Motivated by well-known obstacles to quantum gravity, I look for the most general geometrodynamical symmetries compatible with a reduced physical configuration space for metric gravity. I argue that they lead either to a completely static…

We describe, up to isomorphism, all locally simple subalgebras of any diagonal locally simple Lie algebra.

A cohomology theory, associated to a $n$-Lie algebra and a representation space of it, is introduced. It is observed that this cohomology theory is qualified to encode the generalized derivation extensions, and that it coincides, for $n=3$,…

Let $F$ be a non-archimedean local field of residue characteristic $p\neq 2$. Let $G$ be a connected reductive group over $F$ that splits over a tamely ramified extension of $F$. Yu constructed types which are called tame supercuspidal…

We approach the classification of Lie bialgebra structures on simple Lie algebras from the viewpoint of descent and non-abelian cohomology. We achieve a description of the problem in terms faithfully flat cohomology over an arbitrary ring…

We prove a graded version of Alev-Polo's rigidity theorem: the homogenization of the universal enveloping algebra of a semisimple Lie algebra and the Rees ring of the Weyl algebras $A_n(k)$ cannot be isomorphic to their fixed subring under…

We study the L-infinity-formality problem for the Hochschild complex of the universal enveloping algebra of some examples of Lie algebras such as Cartan-3-regular quadratic Lie algebras (for example semisimple Lie algebras and in more…

We give natural descriptions of the homology and cohomology algebras of regular quotient ring spectra of even E-infinity ring spectra. We show that the homology is a Clifford algebra with respect to a certain bilinear form naturally…

The strong homotopy Lie algebra, controlling simultaneous deformations of a morphism of associative algebras and its domain and codomain is constructed. Isomorphism of the cohomology of this strong homotopy Lie algebra with the classical…

The purpose of this paper is to bring together various loose ends in the theory of integrable systems. For a semisimple Lie algebra $\mathfrak g$, we obtain several results on completeness of homogeneous Poisson-commutative subalgebras of…

We investigate homological properties of perfect algebras of prime characteristic. The principle is as follows: perfect algebras resolve the singularities. For example, we show any module over the ring of absolute integral closure has…

We describe representations of certain superconformal algebras in the semi-infinite Weil complex related to the loop algebra of a complex finite-dimensional Lie algebra and in the semi-infinite cohomology. We show that in the case where the…

Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play important roles in mathematical physics. This survey article…

We generalize all known results on rigidity of uniform Roe algebras to the setting of arbitrary uniformly locally finite coarse spaces. For instance, we show that isomorphism between uniform Roe algebras of uniformly locally finite coarse…

We prove that for generalised partitions of unity ${\phi_i \mid i \in I}$ and coverings $\mathfrak{U}:={\phi_i^{-1} (R \setminus {0}) \mid i \in I}$ of a topological space $X$ the cohomology of abstract $\mathfrak{U}$-local cochains…

The notion of Lie $H$-pseudoalgebra is a higher-dimensional analogue of Lie conformal algebras. In this paper, we classify the equivalence classes of non-abelian extensions of a Lie $H$-pseudoalgebra $L$ by another Lie $H$-pseudoalgebra $M$…