Related papers: Graphical introduction to classical Lie algebras

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 initiate a study on a range of new generalized derivations of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. This new generalization of derivations has an analogue in the theory of associative…

The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…

The syntax of modal graphs is defined in terms of the continuous cut and broken cut following Charles Peirce's notation in the gamma part of his graphical logic of existential graphs. Graphical calculi for normal modal logics are developed…

This is an old paper put here for archeological purposes. We derive a general formula expressing the second homology of a Lie algebra of the form L\otimes A with coefficients in the trivial module through homology of $L$, cyclic homology of…

In this paper, we mainly study some properties of elementary n-Lie algebras, and prove some necessary and sufficient conditions for elementary n-Lie algebras, we also give the relations between elementary n-algebras and E-algebras.

This is a survey work on Lie algebras with ad-invariant metrics. We summarize main features, notions and constructions, in the aim of bringing into consideration the main research on the topic. We also give some list of examples in low…

We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an…

We give a concise introduction to (discrete) algebras arising from \'etale groupoids, (aka Steinberg algebras) and describe their close relationship with groupoid C*-algebras. Their connection to partial group rings via inverse semigroups…

I introduce yet another way to associate a C*-algebra to a graph and construct a simple nuclear C*-algebra that has irreducible representations both on a separable and a nonseparable Hilbert space.

We compute the index of a Lie Borel Lie Algbra of a simple Lie algebra.

We introduce the notion of a conformal pseudo-subriemannian fundamental graded Lie algebra of semisimple type. Moreover we give a classification of conformal pseudo-subriemannian fundamental graded Lie algebras of semisimple type and their…

A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…

When the theory of Leavitt path algebras was already quite advanced, it was discovered that some of the more difficult questions were susceptible to a new approach using topological groupoids. The main result that makes this possible is…

We present a construction of 2-step nilpotent Lie algebras using labeled directed simple graphs, which allows us to give a criterion to detect certain ideals and subalgebras by finding special subgraphs. We prove that if a label occurs only…

In this paper, we introduce the solvabilizer and the solvable graph for a Lie superalgebra and establish their basic properties. Then we define a category which links Lie superalgebras to their solvable substructures. Afterwards, we prove…

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…

We investigate the notion of real form of complex Lie superalgebras and supergroups, both in the standard and graded version. Our functorial approach allows most naturally to go from the superalgebra to the supergroup and retrieve the real…

We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the…

We construct the Lie algebra of an n-Lie algebra and we also define the notion of cohomology of an n-Lie algebra.