Generalized Blob Algebras and Alcove Geometry

Generalized Blob Algebras and Alcove Geometry

Noncommutative Differential Geometry of Generalized Weyl Algebras

Elements of noncommutative differential geometry of Z-graded generalized Weyl algebras A(p; q) over the ring of polynomials in two variables and their zero-degree subalgebras B(p; q), which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed. In particular, three classes of skew derivations of A(p; q) are constructed, and three-dimensional first-...

Non-smooth differential geometry and algebras of generalized functions

Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in this field and highlights some applications in mathematical physics. Mathematics Subject Classification (2000): Primary: 46F30; secondary: 46T30, 53B20.

Generalized Witt Algebras and Generalized Poisson Algebras

It is well known that the Poisson Lie algebra is isomorphic to the Hamiltonian Lie algebra [1],[3],[13]. We show that the Poisson Lie algebra can be embedded properly in the special type Lie algebra [13]. We also generalize the Hamitonian Lie algebra using exponential functions, and we show that these Lie algebras are simple.

On Lorentz Geometry in Algebras of Generalized Functions

We introduce a concept of causality in the framework of generalized pseudo-Riemannian Geometry in the sense of J.F. Colombeau and establish the inverse Cauchy-Schwarz inequality in this context. As an application, we prove a dominant energy condition for some energy tensors as put forward in Hawking and Ellis’s book “The large scale structure of space-time”. Our work is based on a new character...