相关论文: Ideals in non-associative universal enveloping alg…

Given a unital associative ring S and a subring R, we say that S is an ideal (or Dorroh) extension of R if for some ideal I of S, S = R + I, where the sum is direct. In this note we investigate the ideal structure of an arbitrary ideal…

The Lie algebra of infinitesimal isometries of a Riemannian manifold contains at most two commutative ideals. One coming from the horizontal nullity space of the Nijenhuis tensor of the canonical connection, the other coming from the…

We present two constructions of complex symplectic structures on Lie algebras with large abelian ideals. In particular, we completely classify complex symplectic structures on almost abelian Lie algebras. By considering compact quotients of…

New commutative subalgebras of the maximal Gel'fand-Kirillov dimension in the universal enveloping algebras of classical Lie algebras gl(n) and so(n) are constructed. In the case of sp(n) Gel'fand-Tsetlin algebra is extended to a maximally…

The goal of this work is to study the ideals of the Goldman Lie algebra $S$. To do so, we construct an algebra homomorphism from $S$ to a simpler algebraic structure, and focus on finding ideals of this new structure instead. The structure…

In this work, we consider Lie algebras L containing a subalgebra isomorphic to sl3 and such that L decomposes as a module for that sl3 subalgebra into copies of the adjoint module, the natural 3-dimensional module and its dual, and the…

Following Robert's [26], we study the structure of unitary groups and groups of approximately inner automorphisms of unital $C^*$-algebras, taking advantage of the former being Banach-Lie groups. For a given unital $C^*$-algebra $A$, we…

A new class of infinite dimensional simple Lie algebras over a field with characteristic 0 are constructed. These are examples of non-graded Lie algebras. The isomorphism classes of these Lie algebras are determined. The structure space of…

Lie algebras endowed with an action by automorphisms of any of the symmetric groups S3 or S4 are considered, and their decomposition into a direct sum of irreducible modules for the given action is studied. In case of S3-symmetry, the Lie…

We study some applications of solvable Lie algebras in type IIA, type IIB and M theories. RR and NS generators find a natural geometric interpretation in this framework. Special emphasis is given to the counting of the abelian nilpotent…

S-expansions of three-dimensional real Lie algebras are considered. It is shown that the expansion operation allows one to obtain a non-unimodular Lie algebra from a unimodular one. Nevertheless S-expansions define no ordering on the…

Let $L$ be a restricted Lie algebra over a field of characteristic $p>2$ and denote by $u(L)$ its restricted enveloping algebra. We establish when the symmetric or skew elements of $u(L)$ under the principal involution are Lie metabelian.

Perfect ideals $I$ of grade $3$ in a local ring $(R,\mathfrak{m},\Bbbk)$ can be classified based on multiplicative structures on $\text{Tor}^R_{\bullet}(R/I,\Bbbk)$. The classification is incomplete in the sense that it remains open which…

For each simple symplectic triple system over the real numbers, the standard enveloping Lie algebra and the algebra of inner derivations of the triple provide a reductive pair related to a semi-Riemannian homogeneous manifold. It is proved…

Absolute algebras are a new type of algebraic structures, endowed with a meaningful notion of infinite sums of operations without supposing any underlying topology. Opposite to the usual definition of operadic calculus, they are defined as…

The Calabi-Yau property of cocommutative Hopf algebras is discussed by using the homological integral, a recently introduced tool for studying infinite dimensional AS-Gorenstein Hopf algebras. It is shown that the skew-group algebra of a…

In this paper we continue the study of the subalgebra lattice of a Leibniz algebra. In particular, we find out that solvable Leibniz algebras with an upper semi-modular lattice are either almost-abelian or have an abelian ideal spanned by…

Lie conformal algebras are useful tools for studying vertex operator algebras and their representations. In this paper, we establish close relations between Poisson conformal algebras and representations of Lie conformal algebras. We also…

We study the structure of graded Lie superalgebras with arbitrary dimension and over an arbitrary field ${\mathbb K}$. We show that any of such algebras ${\mathfrak L}$ with a symmetric $G$-support is of the form ${\mathfrak L} = U +…

Let G be a nilpotent p-valuable (compact p-adic Lie) group. There is an ongoing investigation into the prime ideals of its completed group algebra (Iwasawa algebra), and there remains an open conjecture that they can all be proved to have a…