Recent Advances of Lie Theory in differential Geometry, in memory of John Nash | Journal of Generalized Lie Theory and Applications

Journal of Generalized Lie Theory and Applications

ISSN: 1736-4337

Open Access

Research Article

Pages: 0 - 0

On Representations of Bol Algebras

Ndoune N and Bouetou Bouetou T

In this paper, we introduce the notion of representation of Bol algebra. We prove an analogue of the classical Engel’s theorem and the extension of Ado-Iwasawa theorem for Bol Algebras. We study the category of representations of Bol algebras and show that it is a tensor category. In the case of regular representations of Bol algebras, we give a complete classification of them for all two-dimensional Bol algebras.

Research Article

Pages: 0 - 0

A Lie Algebraic and Numerical Investigation of the Black-Scholes Equation with Heston Volatility Model

Merger J and Borzi A

This work deals with an extension of the Black-Scholes model for rating options with the Heston volatility model. A Lie-algebraic analysis of this equation is applied to reduce its order and compute some of its solutions. As a result of this method, a five-parameter family of solutions is obtained. Though, these solutions do not match the terminal and boundary conditions, they can be used for the validation of numerical schemes.

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