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- W2046338664 endingPage "012020" @default.
- W2046338664 startingPage "012020" @default.
- W2046338664 abstract "In the present paper we review the progress of the project of classification and construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we called earlier 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduced recently the new notion of parabolic relation between two non-compact semisimple Lie algebras G and G' that have the same complexification and possess maximal parabolic subalgebras with the same complexification. Thus, we consider the exceptional algebra E7(7) which is parabolically related to the CLA E7(−25). Other interesting examples are the orthogonal algebras so(p, q) all of which are parabolically related to the conformal algebra so(n, 2) with p + q = n + 2, the parabolic subalgebras including the Lorentz subalgebra so(n − 1,1) and its analogs so(p − 1, q − 1). Further we consider the algebras sl(2n, ) and for n = 2k the algebras su* (4k) which are parabolically related to the CLA su(n,n). Further we consider the algebras sp(r,r) which are parabolically related to the CLA sp(2r, ). We consider also E6(6) and E6(2) which are parabolically related to the hermitian symmetric case E6(-14)," @default.
- W2046338664 created "2016-06-24" @default.
- W2046338664 creator A5044713068 @default.
- W2046338664 date "2014-05-12" @default.
- W2046338664 modified "2023-09-27" @default.
- W2046338664 title "Classification of Invariant Differential Operators for Non-Compact Lie Algebras via Parabolic Relations" @default.
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