منابع مشابه
On the Classification of Automorphic Lie Algebras
It is shown that the problem of reduction can be formulated in a uniform way using the theory of invariants. This provides a powerful tool of analysis and it opens the road to new applications of these algebras, beyond the context of integrable systems. Moreover, it is proven that sl2(C)–Automorphic Lie Algebras associated to the icosahedral group I, the octahedral group O, the tetrahedral grou...
متن کاملAutomorphic Lie Algebras with Dihedral Symmetry
Automorphic Lie Algebras are interesting because of their fundamental nature and their role in our understanding of symmetry. Particularly crucial is their description and classification as it allows us to understand and apply them in different contexts, from mathematics to physical sciences. While the problem of classification of Automorphic Lie Algebras with dihedral symmetry was already cons...
متن کاملAutomorphic Orbit Problem for Polynomial Algebras
It is proved that every endomorphism preserving the automorphic orbit of a nontrivial element of the rank two polynomial algebra over the complex number field is an automorphism.
متن کاملReduction Groups and Automorphic Lie Algebras
We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates the name automorphic Lie algebras. For automorphic Lie algebras we present bases in which they are quasigraded and all structure constants can be written out e...
متن کاملRemarks on Finite W Algebras
The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G ≃ so(4, 2), unitary representations of the conformal and Poincaré algebras are recognized in this approach, which can be compared to the usual induced representation technique. When G ≃ sp(2,R) or sp(4,R ), the anyonic parameter can be se...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1969
ISSN: 0019-2082
DOI: 10.1215/ijm/1256053423