Related papers: Centralizing traces and Lie triple isomorphisms on…

Let $G$ be the Lie group $SO_e(4,1)$, with maximal compact subgroup $K = S(O(4) \times O(1))_e\cong SO(4)$. Let $\mathfrak{g}=\mathfrak{so}(5,\mathbb{C})$ be the complexification of the Lie algebra $\mathfrak{g}_0 = \mathfrak{so}(4,1)$ of…

In this two-part series of articles, we present a new proof comparing the trace formula for a general linear group with that of one of its inner forms. Our methodology relies on the trace formula for Lie algebras, incorporating the notion…

We develop several applications of the fact that the Yokonuma--Hecke algebra of the general linear group GL is isomorphic to a direct sum of matrix algebras associated to Iwahori--Hecke algebras of type A. This includes a description of the…

Let $\mathfrak{g}$ be a reductive Lie algebra over an algebraically closed, characteristic zero field or over $\mathbb{R}$. Let $\mathfrak{q}$ be a parabolic subalgebra of $\mathfrak{g}$. We characterize the derivations of $\mathfrak{q}$ by…

In this work large families of naturally graded nilpotent Lie algebras in arbitrary dimension and characteristic sequence (n,q,1), with n odd, satisfying the centralizer property, are given. This condtion constitutes a generalization, for a…

Let $\mathcal{B}_{\mathfrak{q}}$ be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix $\mathfrak{q} \in \mathbf{k}^{\theta \times \theta}$, where $\mathbf{k}$ is an algebraically closed field of characteristic…

Motivated by the Cheung's elaborate work [Linear Multilinear Algebra, 51 (2003), 299-310], we investigate the construction of a Lie derivation on a generalized matrix algebra and apply it to give a characterization for such a Lie derivation…

For any decomposition of a Lie superalgebra $\mathcal G$ into a direct sum $\mathcal G=\mathcal H\oplus\mathcal E$ of a subalgebra $\mathcal H$ and a subspace $\mathcal E$, without any further resctrictions on $\mathcal H$ and $\mathcal E$,…

This paper describes the centers of the universal enveloping algebras and the invariant rings of the standard filiform Lie algebras over fields of characteristic zero and also over large enough prime characteristic. We determine explicit…

Let G be a semisimple algebraic group over a field K whose characteristic is very good for G, and let sigma be any G-equivariant isomorphism from the nilpotent variety to the unipotent variety; the map sigma is known as a Springer…

Let $G$ be a finite group and $R$ be a commutative ring. The Mackey algebra $\mu_{R}(G)$ shares a lot of properties with the group algebra $RG$ however, there are some differences. For example, the group algebra is a symmetric algebra and…

For any locally compact group $G$ and any Banach algebra $A$, a characterization of the closed Lie ideals of the generalized group algebra $L^1(G,A)$ is obtained in terms of left and right actions by $G$ and $A$. In addition, when $A$ is…

Let i be a homomorphism of the multiplicative group into a connected reductive algebraic group over C. Let G^i be the centralizer of the image i. Let LG be the Lie algebra of G and let L_nG (n integer) be the summands in the direct sum…

The spectrum of an admissible subalgebra $\mathscr{A}(G)$ of $\mathscr{LUC}(G)$, the algebra of right uniformly continuous functions on a locally compact group $G$, constitutes a semigroup compactification $G^\mathscr{A}$ of $G$. In this…

Given any K\"ahler manifold $X$, Kapranov discovered an $L_\infty[1]$ algebra structure on $\Omega^{0,\bullet}_X(T^{1,0}_X)$. Motivated by this result, we introduce, as a generalization of $L_\infty[1]$ algebras, a notion of $L_\infty[1]$…

In this paper, Lie bialgebra structures on generalized Heisenberg-Virasoro algebra $\mathfrak{L}$ are considered. Also, $H^1({\mathfrak{L}} ,\mathfrak{L}\bigotimes\mathfrak{L})$ is given explicitly. Moreover, it is proved that all Lie…

A new highly symmetrical model of the compact Lie algebra $\mathfrak{g}^c_2$ is provided as a twisted ring group for the group $\mathbb{Z}_2^3$ and the ring $\mathbb{R}\oplus\mathbb{R}$. The model is self-contained and can be used without…

We prove that for q not a nontrivial root of unity any symmetric invariant 2-cocycle for a completion of Uq(g) is the coboundary of a central element. Equivalently, a Drinfeld twist relating the coproducts on completions of Uq(g) and U(g)…

The aim of this work is to investigate the structure of some skew twisted algebras, when the coefficient ring is a localization of the polynomial ring over the field of characteristic zero, and an involution is provided. A parallel…

For simple Lie algebras of types B, C, and D, we provide new explicit formulas for the generators of the Feigin-Frenkel centre. These formulas make use of the symmetrisation map as well as some well-chosen symmetric invariants of $\mathfrak…