Author(s): Dongho Moon
Series: PhD thesis at University of Wisconsin-Madison
Year: 1998
Abstract
Acknowledgements
1 Introduction
2 Tensor product representations of the Lie superalgebra p(n) and
their centralizers
2.1 The Lie superalgebra p(n) .......................
2.2 The commuting actions on the p(n)-module V®k ...........
2.3 Maximal vectors of p(n) in V®’c ....................
2.4 The algebra Ak as the centralizer algebra of p(n) ...........
2.5 The ring structure of A,‘ ........................
2.6 The decomposition of V” .......................
2.6.1 Decomposition of V82 .....................
2.6.2 Decomposition of V“ .....................
2.6.3 Non-complete reducibility of V“ ...............
3 The centralizer algebras of Lie color algebras
3.1 Preliminaries ..............................
3.2 Lie color algebras and Lie superalgebras ...............
3.3 Some simple Lie color algebras ....................
3.3.1 Special linear Lie color algebras ................
ii
iv
6
6
25
32
43
47
47
54
60
70
71
3.4
3.5
3.6
3.7
3.8
vii
3.3.2 Subalgebras of 91 (V, s) which leave invariant an e—symmetric
bilinear form on V ....................... 73
3.3.3 The family psq(V, e) ...................... 77
The Representation Theory of Lie Color Algebras .......... 81
End(V®") and the centralizer algebra ................. 85
Centralizer algebra of 91 (V, e) ..................... 89
The Centralizer Algebra of sq(V, e) .................. 97
Application: Decomposition of the free Lie color algebra ...... 101
Bibliography 105
