New Lie-Algebraic and Quadratic Deformations of Minkowski Space from Twisted Poincare Symmetries

We consider two new classes of twisted D=4 quantum Poincar\'{e} symmetries described as the dual pairs of noncocommutative Hopf algebras. Firstly we investigate a two-parameter class of twisted Poincar\'{e} algebras which provide the examples of Lie-algebraic noncommutativity of the translations. The corresponding associative star-products and new deformed Lie-algebraic Minkowski spaces are introduced. We discuss further the twist deformations of Poincar\'{e} symmetries generated by the twist with its carrier in Lorentz algebra. We describe corresponding deformed Poincar\'{e} group which provides the quadratic deformations of translation sector and define the quadratically deformed Minkowski space-time algebra.