4 research outputs found
On Lie-algebraic solutions of the type IIB matrix model
A systematic search for Lie algebra solutions of the type IIB matrix model is
performed. Our survey is based on the classification of all Lie algebras for
dimensions up to five and of all nilpotent Lie algebras of dimension six. It is
shown that Lie-type solutions of the equations of motion of the type IIB matrix
model exist and they correspond to certain nilpotent and solvable Lie algebras.
Their representation in terms of Hermitian matrices is discussed in detail.
These algebras give rise to certain non-commutative spaces for which the
corresponding star-products are provided. Finally the issue of constructing
quantized compact nilmanifolds and solvmanifolds based on the above algebras is
addressed.Comment: 22 page
Four-dimensional compact projective planes of orbit type (1,1)
We consider 4-dimensional flexible projective planes with the following properties: The collineation group is a 6-dimensional solvable Lie group which fixes some flag â â W. Furthermore, the collineation group has a 1-dimensional orbit both on W and on the pencil of lines through {â}. We show that there are three different families of planes with these properties.Betten, Dieter; Polster, Burkar