Generalized Yangians and their Poisson counterparts

Yangians and Their Applications *

Yangians: their Representations and Characters

The Yangian Y (g) associated to a finite-dimensional complex simple Lie algebra g is a Hopf algebra deformation of the universal enveloping algebra of the Lie algebra g[u] of polynomial maps C → g (with Lie bracket defined pointwise). It is important to understand the finite-dimensional representations of Y (g). For one thing, they are closely related to rational solutions of the so-called quan...

Generalized Davenport-Schinzel sequences and their 0-1 matrix counterparts

Article history: Received 8 August 2010 Available online xxxx

Lie Bialgebra Structures on Twodimensional Galilei Algebra and Their Lie–poisson Counterparts

All bialgebra structures on twodimensional Galilei algebra are classified. The corresponding Lie–Poisson structures on Galilei group are found. ∗Supported by the Lódź University Grant No.487

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.