Lie bialgebra structures on the Schrödinger–Virasoro Lie algebra

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

Lie bialgebra structures on the W - algebra W ( 2 , 2 ) 1

Abstract. Verma modules over the W -algebra W (2, 2) were considered by Zhang and Dong, while the Harish-Chandra modules and irreducible weight modules over the same algebra were classified by Liu and Zhu etc. In the present paper we shall investigate the Lie bialgebra structures on the referred algebra, which are shown to be triangular coboundary.

L∞ algebra structures of Lie algebra deformations

In this paper,we will show how to kill the obstructions to Lie algebra deformations via a method which essentially embeds a Lie algebra into Strong homotopy Lie algebra or L∞ algebra. All such obstructions have been transfered to the revelvant L∞ algebras which contain only three terms.

PostLie algebra structures on the Lie Algebra SL(2,Ca)

A New Lie Bialgebra Structure

We describe the Lie bialgebra structure on the Lie superalgebra sl(2, 1) related to an r−matrix that cannot be obtained by a Belavin-Drinfeld type construction. This structure makes sl(2, 1) into the Drinfeld double of a four-dimensional subalgebra. It is well-known that non-degenerate r−matrices (describing quasitriangular Lie bialgebra structures) on simple Lie algebras are classified by Bela...