Related papers: The Dixmier map for nilpotent super Lie algebras
In this paper we introduce the notion of pure non-characteristically nilpotent Lie algebra and under a condition we prove that a complex maximal extension of a finite-dimensional pure non-characteristically nilpotent Lie algebra is…
It is shown that a unital C*-algebra A has the Dixmier property if and only if it is weakly central and satisfies certain tracial conditions. This generalises the Haagerup-Zsido theorem for simple C*-algebras. We also study a uniform…
A Poisson analog of the Dixmier-Moeglin equivalence is established for any affine Poisson algebra $R$ on which an algebraic torus $H$ acts rationally, by Poisson automorphisms, such that $R$ has only finitely many prime Poisson $H$-stable…
The paper considers subspaces of the strictly upper triangular matrices, which are stable under Lie bracket with any upper triangular matrix. These subspaces are called ad-nilpotent ideals and there are Catalan number of such subspaces.…
In the first part of this paper we present explicit formulas for primitive idempotents in arbitrary Frobenius algebras using the entries of representing matrices coming from projective indecomposable modules with respect to a certain choice…
The purpose of this Ph.D. thesis is to study and classify primitive ideals of the enveloping algebras $U(\mathfrak{o}(\infty))$ and $U(\mathfrak{sp}(\infty))$. Let $\mathfrak{g}(\infty)$ denote any of the Lie algebras $\mathfrak{o}(\infty)$…
We introduce the notion of dual perfect bases and dual perfect graphs. We show that every integrable highest weight module $V_q(\lambda)$ over a quantum generalized Kac-Moody algebra $U_{q}(\mathcal{g})$ has a dual perfect basis and its…
Over a field of characteristic zero, we show that two commutative differential graded (dg) algebras are quasi-isomorphic if and only if they are quasi-isomorphic as associative dg algebras. This answers a folklore problem in rational…
In this paper is devoted to nilpotent finite-dimensional evolution algebras E with $dimE^2 = dimE-1$. We described Lie algebras associated with evolution algebras whose nilindex is maximal. Moreover, in terms of this Lie algebra we fully…
Let $n$ be a maximal nilpotent subalgebra of a complex symmetric Kac-Moody Lie algebra. Lusztig has introduced a basis of U(n) called the semicanonical basis, whose elements can be seen as certain constructible functions on varieties of…
This paper explores 3d $\mathcal{N}=4$ quiver gauge theories whose moduli spaces represent nilpotent orbits, S\l odowy slices or, more generally, S\l odowy intersections, which span the Special Pieces of nilcones of Classical or Exceptional…
Let $K$ be a field, let $E$ be a finite directed graph, and let $L_K(E)$ be the Leavitt path algebra of $E$ over $K$. We show that for a prime ideal $P$ in $L_K(E)$, the following are equivalent: \begin{enumerate} \item $P$ is primitive;…
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three…
We describe the prime ideals and, in particular, the maximal ideals in products $R = \prod D_\lambda$ of families $(D_\lambda)_{\lambda \in \Lambda}$ of commutative rings. We show that every maximal ideal is induced by an ultrafilter on the…
In this paper, the $C^*$-algebra of the seven-dimensional un-decomposable nilpotent Lie group is characterized explicitly for the first time(see \cite{chin}). Furthermore, the topology of its spectrum is described as a preparation for the…
We provide a review of results on two-sided ideals in the enveloping algebra U$(\frak g(\infty))$ of a locally simple Lie algebra $\frak g(\infty)$. We pay special attention to the case when $\frak g(\infty)$ is one of the finitary Lie…
A nilpotent Lie algebra n_{n,1} with an (n-1) dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with n_{n,1} as their nilradical are obtained. Their dimension is at most n+2. The generalized Casimir invariants…
Inspired by the commutator and anticommutator algebras derived from algebras graded by groups, we introduce noncommutatively graded algebras. We generalize various classical graded results to the noncommutatively graded situation concerning…
A braided bialgebra is called primitively generated if it is generated as an algebra by its space of primitive elements. We prove that any primitively generated braided bialgebra is isomorphic to the universal enveloping algebra of its…
We study finite-dimensional nonassociative algebras. We prove the implicit function theorem for such algebras. This allows us to establish a correspondence between such algebras and quasigroups, in the spirit of classical correspondence…