We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for the classification of finite-growth contragredient Lie superalgebras. The results of this paper are a crucial part of the proof for the classification of co...

In this paper, we consider an autonomous two-dimensional ODE Kolmogorov-type system with three parameters, which is a particular of the general predator–prey systems Holling type II. By reformulating as set two second-order differential equations, investigate nonlinear dynamics from Jacobi stability point view using Kosambi–Cartan–Chern (KCC) geometric theory. We then determine connection, Berw...

Ghost neutrino solution in radiative Kerr spacetime endowed with totally skew-symmetric Cartan contortion is presented. The computations are made by using the Newman-Penrose (NP) calculus. The model discussed here maybe useful in several astrophysical applications specially in black hole astrophysics. PACS number(s): 0420, 0450 Departamento de F́ısica Teorica-UERJ. Rua São Fco. Xavier 524, Rio d...

We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for the classification of finite-growth contragredient Lie superalgebras. The results of this paper are a crucial part of the proof for the classification of co...

After a brief reminder of the Cartan 1-form and its application to the mechanics of point particles we review the application of Cartan 4-forms to eld theory.

We prove involutivity of Einstein and Einstein-Maxwell equations by calculating the Spencer cohomology of these systems. Relation with Cartan method is traced in details. Basic implications through Cartan-Kähler theory are derived.

Abstract Twisted étale groupoid algebras have recently been studied in the algebraic setting by several authors connection with an abstract theory of Cartan pairs rings. In this paper we show that extensions ample groupoids correspond a precise manner to Boolean inverse semigroups. particular, discrete twists over certain abelian semigroups, and they are classified Lausch’s second cohomology gr...

In this paper, we study the Cartan invariants for rank-one Cartan type Lie algebra W (1, n). This is done by reducing representations of generalized restricted Cartan type Lie algebra W (1, n) to representations of restricted Lie algebras W (1, 1) and of sl(2), and then extending Feldvoss-Nakano’s argument on W (1, 1) to the case W (1, n). Our discussion also shows some surprising difference be...