Cohomology of Dowling Lattices and Lie (Super)Algebras

We extend a well-known relationship between the representation of the symmetric group on the homology of the partition lattice and the free Lie algebra to Dowling lattices.

[1]  M. Scheunert,et al.  The Theory of Lie Superalgebras , 1979 .

[2]  Anne E. Browdy.  The (co)homology of lattices of partitions with restricted block size , 1996 .

[3]  Nantel Bergeron,et al.  The Orlik-Solomon algebra on the partition lattice and the free Lie algebra , 1990, J. Comb. Theory, Ser. A.

[4]  Anders Björner,et al.  Matroid Applications: Homology and Shellability of Matroids and Geometric Lattices , 1992 .

[5]  Jon Folkman,et al.  THE HOMOLOGY GROUPS OF A LATTICE , 1964 .

[6]  Anders Björner,et al.  On the homology of geometric lattices , 1982 .

[7]  Louis Solomon,et al.  On the action of the symmetric group on the cohomology of the complement of its reflecting hyperplanes , 1986 .

[8]  Thomas A. Dowling,et al.  A class of geometric lattices based on finite groups , 1973 .

[9]  Hélène Barcelo,et al.  On the action of the symmetric group on the Free Lie Algebra and the partition lattice , 1990, J. Comb. Theory, Ser. A.

[10]  Michelle L. Wachs.  A Basis for the Homology of thed-Divisible Partition Lattice , 1996 .

[11]  Nantel Bergeron.  A hyperoctahedral analogue of the free lie algebra , 1991, J. Comb. Theory, Ser. A.

[12]  Phil Hanlon,et al.  The characters of the wreath product group acting on the homology groups of the Dowling lattices , 1984 .

[13]  P. Orlik,et al.  Arrangements Of Hyperplanes , 1992 .

[14]  P. Orlik,et al.  Combinatorics and topology of complements of hyperplanes , 1980 .

[15]  P. Hanlon,et al.  On lie k-algebras , 1995 .

[16]  Michelle L. Wachs,et al.  On the (co)homology of the partition lattice and the free Lie algebra , 1998, Discret. Math..

[17]  Kenneth Baclawski,et al.  Whitney Numbers of Geometric Lattices , 1975 .

[18]  Richard P. Stanley,et al.  Some Aspects of Groups Acting on Finite Posets , 1982, J. Comb. Theory, Ser. A.