Setting Hidden Symmetries Free by the Noncommutative Veronese Mapping
نویسنده
چکیده
The note is devoted to the setting free of hidden symmetries in Verma modules over sl(2, C) by the noncommutative Veronese mappings. In many cases the behavior of systems is governed not only by their natural (geometric) symmetries but also by hidden ones. The main difficulty to work with hidden symmetries is that they are often ”packed”, and as a rule can’t be ”unpacked” to the universal envelopping algebras of Lie algebras, so there exists a problem how to set them free ”correctly” (see f.e.[1-3]). That means to find a ”correct” algebraic structure, which is represented by them. This is one of the themes of this short note. It maybe considered as preliminary to the second one, which is related to a view of the noncommutative geometry [1] on the setting hidden symmetries free. The most interesting setting free mappings are noncommutative Veronese mappings (certain analogs of classical ones [4]); on such way the problem of the noncommutative ”birational” equivalence of the differently obtained set free hidden symmetries is appeared (cf.[5]). Both marked subjects are interacted in the paper on the simplest examples of hidden symmetries in Verma modules over sl(2,C). I wish to thank Prof. J.-L.Gervais and the collective of LPTENS for a kind hospitality and sincere atmosphere during my work on the note.
منابع مشابه
Topics in Hidden Symmetries. Iii.
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