NOTTINGHAM ALGEBRA WITH DIAMOND OF FINITE AND INFINITE TYPE
Thin Lie algebras are infinite-dimensional graded Lie algebras L = L? i=1, where Li’s is a subspace of L called a homogeneous component. The first homogeneous component is two-dimensional and equipped with a covering property, which results in its homogeneous components having no more than two...
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| 格式: | Final Project |
| 語言: | Indonesia |
| 在線閱讀: | https://digilib.itb.ac.id/gdl/view/64811 |
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| 機構: | Institut Teknologi Bandung |
| 語言: | Indonesia |
| 總結: | Thin Lie algebras are infinite-dimensional graded Lie algebras L =
L?
i=1, where
Li’s is a subspace of L called a homogeneous component. The first homogeneous
component is two-dimensional and equipped with a covering property, which results
in its homogeneous components having no more than two dimensions. The twodimensional
homogeneous component is called a diamond. Hence the first homogeneous
component is the first diamond. It has been well-known that the degree of the
second diamond can only be 3, 5, q, or 2q?1, where q is a power of the field characteristic.
We will give more straightforward proof regarding the possible values for
the degree of the second diamond.
Nottingham algebras are thin Lie algebras whose degree of the second diamond
is in the form q. In Nottingham algebras, every diamond except the first can be
assigned to a type that belongs to the underlying field or is equal to?. We will give
general structure to the Nottingham algebras, such as the pattern of the types on the
diamonds and the distance between the diamonds. We will also construct a class of
Nottingham algebras as loop algebras of Hamiltonian algebras H(2 : (s+1, n); ?0)
of Cartan type. One can show that the exponential of a nilpotent derivation gives
new grading for a graded Lie algebras, such grading switching plays an important
role in our construction. |
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